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### Course: Algebra basics>Unit 2

Lesson 2: Substitution & evaluating expressions

# Evaluating expressions with two variables

We've already evaluated expressions with one variable. Now it's time to do it with two variables.
Khan Academy video wrapper
Evaluating expressions with two variablesSee video transcript

## How to evaluate an expression with two variables

Let's say we want to evaluate the expression $10+2p-3r$. Well, first we need to know the values of $p$ and $r$. For example, to evaluate the expression when $p=4$ and $r=5$, we just replace $p$ with $4$ and $r$ with $5$:
$\phantom{=}10+2p-3r$
$=10+2\cdot 4-3\cdot 5$
$=10+8-15$
$=3$
So, the expression $10+2p-3r$ equals $3$ when $p=4$ and $r=5$.

## Now, let's practice

Problem 1
Evaluate $6a+4b-6$ when $a=1$ and $b=3$.

## Want to join the conversation?

• On the first question, it says my answer is wrong and I got 18 as my answer.
(86 votes)
• At first i got that too, but then i realized there was a -6 at the end of the problem. So the actual answer was 12. :)
(137 votes)
• i dont get the 2nd q how do we solve it when its an fraction
(17 votes)
• a fraction is division. so 10 divided by 5 can be written as a fraction 10/5, and x/y means x divided by y. does that help? you would do it along with multiplication in the order of operations.
(42 votes)
• easy peasy lemon squezy
(23 votes)
• yup yup yup
(3 votes)
• how do you expand and simplify: 2(x- 1)(x+1)+(2x-1)(2x-1)
(12 votes)
• First distribute 3x over (2x+5) and then distribute -2x over (x-6):
3x(2x+5) - 2x(x-6)
= 6x^2 + 15x - 2x^2 + 12x [Note: -2x * -6 = +12x, not -12x]
= 6x^2 - 2x^2 + 15x + 12x [Rewrite with like terms in order.]
= 4x^2 + 27x
(22 votes)
• how can i find the answer in the equation 5x - x/y when x=4 and y =2
(10 votes)
• 1) Substitute each value into the expression for their respective variable
5(4) - 4/2
2) Follow PEMDAS
-- Multiply: 20 - 4/2
-- Divide: 20 - 2
-- Subtract: 18
Hope this helps.
(17 votes)
• how is it not 18
(8 votes)
• Assuming you are asking about the 1st practice exercise... If you got an answer of 18, you ignored the -6 on the right side.
6(1)+4(3-6 = 6+12-6 = 18-6 = 12

Hope this helps.
(13 votes)
• After coming back from the Holiday BELIEVE ME! I had to go through these problems more than (2)- (3) times. Knowing how much I love math this, probably was one of the toughest days ever. This is how I solved the First and second problems:

10+2p-3k ( p=4, r=5)
10 +2*4-3*5
10+8-15
18-15=3

6a+4b-6 ( a=1, b=3)
6*1+4*3-6
6+12-6
18-6=12
(13 votes)
• That is correct! Great job!
(2 votes)
• are we always gonna be shown the numbers the variables represent when doing the work?
(9 votes)
• With these types of problems, yes you would be given the values to use.

You will also learn how to simplify the expressions (where values are not given), and that becomes the basis for learning how to solve algebraic equations where you can solve to find the value for the variable.
(2 votes)
• How come when evaluating expressions with two variables (the previous section) that the minus was completed prior to the plus. The questions was xy - y + 3x where x = 3 and y =2. BOMDAS 3 x 2 - 2 + 3 x 3 =
6 - 2 + 9
6 - 11
(5 votes)
• xy-y+3x , if x=3 and y=2 results to 6 - 2 + 9 = 13.

Either a parenthesis in the exercise got lost or the solution is wrong,
but for the given expression the above result is the correct solution.
(14 votes)
• does the BODMAS order of operations apply here? because i tried doing these exercises by applying addition before subtraction and it gives a different answer
(3 votes)
• BODMAS applies when evaluating / simplifying all expressions. But, you are making a common mistake. People use the acronym too literally. There are 4 steps, not 6.

B = Brackets or Parentheses: Do all work inside parentheses / grouping symbols

O = Orders or Exponents & radicals

DM = Divide & Multiple from left to right. This is one rule/step. It is not divide then multiple. Which every is on the left gets done 1st.

AS = Add & Subtract from left to right. Again, this is one rule/step. It is not add then subtract. Which every operation is on the left gets done first. If the subtraction is on the left in the problem, then it comes before the addition.

Hope this helps.
(16 votes)