How do you substitute y equals 6x-5 and y equals -x plus 9?

Answer 1

This is a relatively simple problem, when spread out in front of you. Let's start with:

Y=6X-5

Y=-X+9 or Y=9-X

Since we know that both expressions are equal to Y, they are therefore logically equal to each other as well. When we set them equal to each other, we get:

6X-5=9-X

Next, we get all of the X terms on one side:

7X-5=9

Finally, get all of the constants on the other side.

7X= 14

Now simply solve for X by dividing both sides by the coefficient of X (in this case 7)

X=2

Now that we know what X is equal to, we return to one of our Y= equations. Either one will do, if we did it right they should both equal the same thing. I'll do both here, as a check that we didn't make any arithmetic errors.

Y=6X-5 Y=9-X

Y=6(2)-5 Y=9-(2)

Y=12-5 Y= 7

Y=7

Since both Y's match, we know that we did it properly! In this system of equations, Y is equal to 7 and X is equal to 2