Main content

## 8th grade (Eureka Math/EngageNY)

### Course: 8th grade (Eureka Math/EngageNY) > Unit 4

Lesson 4: Topic D: Systems of linear equations and their solutions- Systems of equations: trolls, tolls (1 of 2)
- Systems of equations: trolls, tolls (2 of 2)
- Testing a solution to a system of equations
- Solutions of systems of equations
- Systems of equations with graphing
- Systems of equations with graphing
- Systems of equations with graphing: 5x+3y=7 & 3x-2y=8
- Systems of equations with graphing: y=7/5x-5 & y=3/5x-1
- Systems of equations with graphing: chores
- Systems of equations with graphing
- Systems of equations with elimination: 3t+4g=6 & -6t+g=6
- Systems of equations with elimination
- Systems of equations with elimination: x+2y=6 & 4x-2y=14
- Systems of equations with elimination: -3y+4x=11 & y+2x=13
- Systems of equations with elimination: 2x-y=14 & -6x+3y=-42
- Systems of equations with elimination: 4x-2y=5 & 2x-y=2.5
- Systems of equations with elimination: x-4y=-18 & -x+3y=11
- Systems of equations with elimination
- Systems of equations with elimination: 6x-6y=-24 & -5x-5y=-60
- Systems of equations with elimination challenge
- Systems of equations with substitution: 2y=x+7 & x=y-4
- Systems of equations with substitution
- Systems of equations with substitution: y=4x-17.5 & y+2x=6.5
- Systems of equations with substitution: -3x-4y=-2 & y=2x-5
- Systems of equations with substitution: 9x+3y=15 & y-x=5
- Systems of equations with substitution
- Systems of equations with substitution: y=-5x+8 & 10x+2y=-2
- Systems of equations with substitution: y=-1/4x+100 & y=-1/4x+120
- Systems of equations with elimination: apples and oranges
- Systems of equations with elimination: TV & DVD
- Systems of equations with elimination: King's cupcakes
- Systems of equations with elimination: Sum/difference of numbers
- Systems of equations with elimination: potato chips
- Systems of equations with elimination: coffee and croissants
- Systems of equations with substitution: coins
- Systems of equations with substitution: potato chips
- Systems of equations with substitution: shelves
- Systems of equations word problems
- Age word problem: Imran
- Age word problem: Ben & William
- Age word problem: Arman & Diya
- Age word problems
- Solutions to systems of equations: consistent vs. inconsistent
- Systems of equations number of solutions: fruit prices (1 of 2)
- Systems of equations number of solutions: fruit prices (2 of 2)
- Systems of equations number of solutions: y=3x+1 & 2y+4=6x
- Solutions to systems of equations: dependent vs. independent
- Number of solutions to a system of equations graphically
- Number of solutions to a system of equations graphically
- Forming systems of equations with different numbers of solutions
- Number of solutions to a system of equations algebraically
- Comparing Celsius and Fahrenheit temperature scales
- Converting Fahrenheit to Celsius

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Systems of equations with elimination: Sum/difference of numbers

Sal finds two numbers that sum to 70 and have a difference of 24. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- someone please explain this to me(4 votes)
- Like Sir Cumference said, just watch the previous videos. You shouldn't skip around otherwise you'll miss something...(2 votes)

- at0:33if we assume that y is larger than x then, by calculation, solution is (23, 47). Is this valid?(5 votes)
- actually yes(1 vote)

- Can you use the elimination method to find out the two "sum & product" numbers? And if so, how?

Example of a worded question: The sum of two numbers is -42 and the product is -1. What are the two numbers?

Another example: The product of two numbers is equivalent to hundred-eight. The sum of the same two numbers is equal to twenty-four. Find out the two numbers.(5 votes)- 6 * (-7) = -42

6 + (-7) = -1

The two numbers are: 6 and -7

Well I guess the addition elimination method can't be used in this case.(1 vote)

- in the question shouldn't it say find the one number not two numbers?(2 votes)
- Doesn't have to be. This is more like a complex way of elimination. But what you're thinking of is correct too.(4 votes)

- What is the missing number 1,16,-----100,169(2 votes)
- That would 49. Each number is the square of 1, 4, 7, 10 ,13 respectively.(2 votes)

- i watched tis video and it confused me all the way to the end can some onr use english to help me?(2 votes)
- I doubt that anyone can type an answer here that will seem clearer to you than the video. I would suggest you watch the video again, slowly, and make sure you understand what is happening at each step. Maybe do that a couple of times. Keep at it and you will get it. If you are still struggling, a teacher should be able to help you.(2 votes)

- can someone please explain this type of eqation to me, its from one of the exersise things i just dont get it?

EX: Ishaan sells magazine subscriptions and earns $10 for every new subscriber he signs up. Ishaan also earns a $31 weekly bonus regardless of how many magazine subscriptions he sells.

If Ishaan wants to earn at least $74 this week, what is the minimum number of subscriptions he needs to sell?(2 votes)- Ishaan get $10 for every new subscriber, so let x represent the number of new subscribers. So if there were 5 new subscribers, 10(5) = 50 dollars he would earn given $10 for each new subscriber. However, he also earns a weekly bonus of $31, regardless of how many he sells (just for going out on the job and trying :)) So, we could represent his weekly earnings potential by saying 10x + 31. Therefore, if he sold 1 subscription, 10(1) + 31 = $41; if he sold 2 subscriptions,

10(2) + 31 = $51, and so on. Since I know Ishaan wants to earn at least $74, I would write 10x + 31 = 74 and solve. Subtraction 31 from both sides gives me 10x=43; dividing both sides by 10 gives me 4.3 So, if he only sold 4 subscriptions, he would earn $71 [ 10(4) +31 = $71] and if he sold 5 subscriptions he would earn $81 [10(5) + 31 = $81]. Therefore, since he wants to earn at least $74, and he cannot sell a part of a subscription, he must sell 5 new subscriptions in order to earn $74.(2 votes)

- One number is 5 more than 4 times the other and their sum is 10. Find the numbers(2 votes)
- Let us take the first number as x

according to question, we find the second number as=4x+5

Now adding both and equating to their sum we have,

4x+5+x=10

5x=5

x=1

so the two numbers are 1, 9.

Hope i was successful in solving your problem effectively...(2 votes)

- Are there Videos on how to do substitution too because I cant find any(2 votes)
- how to solve: x-4y=24 x-16y=8 using addition by elimination(2 votes)

## Video transcript

Solve using the
elimination method. And they tell us the sum
of two numbers is 70. Their difference is 24. What are the two numbers? So let's use this
first sentence. Let's construct an equation
from this first sentence. Let's construct a constraint. The sum of two numbers. Let's call those
numbers x and y. So their sum, x plus
y, is equal to 70. That's what this first
sentence tells us. The second sentence says
their difference is 24. So that means that x
minus y is equal to 24. We're just going to assume
that x is the larger of the two numbers, and y is
the smaller one. So when you take their
difference like this, you get positive 24. So we have a system of two
equations with two unknowns. And they want us to solve it
using the elimination method. So let's do that. So if we were to just
add these two equations, on the left-hand side, we
would have a positive y, and we would have a
negative y over here. And they would cancel out. So if we were to just
add these two equations, we would be able to
eliminate the y's. So let's do that. So x plus y plus x minus y. Well, the plus y and
the minus y cancel out. And you're just left with
an x plus an x, which is 2x. And then that is going to
be equal to 70 plus 24. 70 plus 24 is 94. And I want to make
it very clear-- and I mentioned it
in previous videos-- that this process of adding the
equations to each other, this is nothing new. We're really just adding the
same thing to both sides. We could do it as to both
sides of this equation. You could say we're adding 24
to both sides of this equation. Over here were explicitly
adding 24 to the 70. And over here you could say
we could add 24 to x plus y, but the second constraint
tells us that x minus y is the same thing as 24. So we're adding the same
thing to both sides. Here we're calling it 24. Here we're calling it x minus y. And we were able
to eliminate the y. So we get 2x is equal to 94. Now we can divide both
sides of this equation by 2. And we are left with x is
equal to-- what is that? 47. And now we can substitute
back into either one of these equations
to solve for y. So let's try this
first one over here. So we have 47 plus
y is equal to 70. We can subtract 47 from
both sides of this equation. So we subtract 47. And we are left with y is
equal to-- what is this? 23. y is equal to 23. And you can verify
that it works. If you add the two numbers, 47
plus 23, you definitely get 70. And then if you take 47 minus
23, you definitely get 24. So it definitely meets
both constraints.