Question

Some help and/or explanation would be greatly appreciated!! :)

Solve the system by substitution.

y= -7x + 15
y= 5x - 9

Answer 1

So, since y= -7x + 15, and it also equals 5x - 9, you can take what y equals (either one works in this scenario) so lets take the 5x - 9. since this is what y equals, you can take that expression and replace y with it in the other equation. After you do this you'd get 5x - 9 = -7x + 15. Now both sides of this equation are equal to y. To find the solution, you solve for the variable. After you do this, you get x = 2. Now that you know what x is, you can plug that into any of the original equations to find y. lets use y = 5x - 9 again. This time, substitute x with the number you found earlier, 2. Then you solve. It should look like this: y = 5(2) - 9. So y is 1. There is your answer, x = 2, y = 1.

Answer 2

y = -7x + 15
y = 5x - 9

You know that y = y because no matter what y equals, it will just be equal to itself. Since y = y, you can set those two expressions equal to each other.

-7x + 15 = 5x - 9 Add 7x to both sides
15 = 12x - 9 Add 9 to both sides
24 = 12x Divide both sides by 12
2 = x

So, now choose one of the original equations (I'll go with y = 5x - 9 because there are no negatives) and plug the newfound x value (2) into it.

y = 5x - 9 Plug in the x-value
y = 5(2) - 9 Multiply
y = 10 - 9 Subtract
y = 1

Now, to check.

y = -7x + 15 Plug in the values
1 = -7(2) + 15 Multiply
1 = -14 + 15 Add
1 = 1

y = 5x - 9 Plug in the values
1 = 5(2) - 9 Multiply
1 = 10 - 9
1 = 1

So, x = 2 and y = 1.