how do i solve these problems using substitution? 1. 2x+y=4 , 3x+y=3 2. x+y=12 ,

Question

how do i solve these problems using substitution?

1. 2x+y=4 , 3x+y=3

2. x+y=12 , 2x+5y=27

3. 4x+y=-1 , 2x-y=-5

4. x+2y=-1 , x+y=2

Explanation / Answer

To solve problems using substitution, you put one variable on one side, all of the other components of the equation on the other side, and then substitute in another equation. Let's look at the first one: #1 2x + y = 4 and 3x + y = 3. The easiest way in this problem is to figure out what y is equal to. Use either equation. I chose to go from 3x + y = 3 to y = 3 - 3x. In this case, you subtract to get y by itself on one side and x and another other constants on the other. When I substitute I like to plug into the equation that I didn't use already. So now 2x + y = 4 becomes 2x + (3 - 3x) = 4, since we determined that y = 3 - 3x. Now solve 2x + 3 - 3x = 4 for x -> -1x = 1 -> x = -1. Plug x = -1 back into one of your original equations to solve for y -> 2x + y = 4 -> 2(-1) + y = 4 -> -2 + y = 4 -> y = 6. Now check your results. 2(-1) + 6 = 4 and 3(-1) + 6 = 3. #2 For this one I'm going to do less chatting and show you the steps, instead. x + y = 12 and 2x + 5y = 27 Easiest to find an equation for x: x = 12 - y from the first equation Plug in to second equation: 2(12 - y) + 5y = 27 -> 24 - 2y + 5y = 27 -> 3y = 3 -> y = 1 Plug y = 1 back into first equation, solve for x: x + 1 = 12 -> x = 11. Check: 11 + 1 = 12 and 2(11) + 5(1) = 27 = 22 + 5 = 27 #3 4x + y = -1 and 2x - y = -5 Find an equation for y: -y = -5 - 2x -> y = 5 + 2x Substitute equation for y into first equation, solve for x: 4x + (5 + 2x) = -1 -> 6x = -6 x = -1 Plug x = -1 back into second equation, solve for y (Note: you can also use the equation you already found to solve for y, in this case, y = 5 + 2x): 2(-1) - y = -5 -> -2 - y = -5 -> -y = -3 -> y = 3. Check: 4(-1) + 3 = -1 -> -4 + 3 = -1 2(-1) - 3 = -5 -> -2 - 3 = -5 #4 x + 2y = -1 and x + y = 2 Find an equation for y: x + y = 2 -> y = 2 - x Plug in to first equation: x + 2(2 - x) = -1 -> x + 4 - 2x = -1 -> -1x = -5 -> x = 5 Use the equation for y to solve for y: y = 2 - 5 -> y = -3 Check: 5 + 2(-3) = -1 -> 5 - 6 = -1 5 + (-3) = 2 -> 5 - 3 = 2 Good luck and feel free to e-mail me if you have any questions :)

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