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# Systems of equations with elimination: apples and oranges

Sal solves a word problem about the price of apples and oranges by creating a system of equations and solving it. Created by Sal Khan.

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• Why was 11 turned into -11 for the bottom problem? I understand the chages to the 5x & 5y but dont understand the change is it because 10 is less than 11?
• The 11 was "turned into" -11, by an operation which prepares the whole equation for the elemination process used later on in order to solve this problem. Essentialy, the whole equation 5x+ 5y = 11 is multiplied by -1 and becomes -5x -5y = -11. This "new equation" still has the same meaning it had before you multiplied it by -1, because you did the same thing to both sides. If you had just multiplied the left side (5x + 5y) by -1, you would have changed the meaning of this equation and the results for x any y you got after the elemination process would have been wrong.
• At , I could not undeerstand why Sal multiplied the bottom equation -1.
• Sal multiplies the bottom equation by -1 to combine the equations and CANCEL out the x values. When he multiples the entire bottom equation by -1 it does NOT change the value of the equation, so he can do this and then add together the equations.

Because he now has a -5x value and a 5x value these two variables cancel out when the equations are added together leaving only the y variable. With one variable left, we can now solve for y.

When you have solved for y using this method, you can then plug that value of y back into an equation and solve for x.

The key here is to narrow the equation down to only one variable somehow. We cannot solve the equation if there is two unknowns.
• three times the larger of two numbers is equal to four times the smaller. the sum of the numbers is 21. find the numbers
• Robert,
You need to convert the words to equations.
The first sentence is
"three times the larger of two numbers is equal to four times the smaller."
First convery the number to number symbols.
"3 times the larger of two numbers is equal to 4 times the smaller."
The words times can be changed to "*"
"3 * the larger of two numbers is equal to 4 * the smaller."
The words "is equal to" can be replaced with an "=" sign.
"3 * the larger of two numbers = 4 * the smaller."
Your unknowns are "the larger of two numbers" and "the smaller"
Let's use the variable L for "the larger " and S for the smaller
3 * L = 4 * S

The second sentence is
"The sum of the numbers is 21"
Sum means add and "the numbers are the same unknowns in the first sentence L and S so
L+S is 21 The is means equals so
L+S = 21

3L = 4S
L+S = 21

I hope that helps make it click for you.
• so easy problem.
1Orange=1dollar and
1Apple=1.2dollar
• I still don't get how to find the other answer do we simpfly?
• You plug in what you got for the first answer into the other variable. Say you are solving 3x+y=10 and you know that y=3. All you have to do is this- 3x+3=10 and solve from there. Simplifying is only necessary at the end when you are dividing.
• so how do I graph this?
• i would just go to desmos and type the equations in. desmos is an online graphing calculator.
• the sum of the two digits in a two digit number equal 7 when reversed the new number is 45 more than the original number what is the new number
• It isn't straightforward to express that in terms of a linear system of equations. This is a different class of problem. There are only 6 numbers to try though that have two digits with digits adding to 7. Just start at 16 and work your way up from there, testing 16, 25, 34, 43, 52, 61. Of course I immediately see that 16 works, so you only have to try one number.
• Is 5x=6?
5x+4y=10
5x+5y=11
so 5x could be 6 and y could be 1
• Yes, You can subtract the first problem from the second problem. You get 5x+5y-5x-4y= 11-10. You are left with 0x-1y=1 or simply y=1. Substitute 1 for y in either equation- I will use the 1st for an example- 5x+(4*1)=10 or 5x+4=10. Subtract 4 from either side and yes you are left with 5x=6 as you asked above. . Solving for x you divide each side by 5 and get x=6/5.
• the thing is wasn’t it obvious enough that you bought one extra orange so an orange would be 1 dollar, 11-10 =1 and then you could’ve just done 11-5 then divided by 5 and got 1.2… why go through the super long process that Sal did to find the answer
• Sal is just trying to give an example how to solve a system of equations, not necessarily is he giving the easiest method.
Also, see until . His wasn't exactly thinking too deeply.
(1 vote)
• How much does it cost to run an 800 watt microwave for 17 hours if the power company charges \$.11 per Kilowatt-hour?