How would i solve for x and y in 3x+2y=17 and 2x-y=2 by using substitution

I’ll do an example problem, and I challenge you to do this on your own!

4x+6y=23

7y-8x=5

Solving for y in 4x+6y=23, we can separate the y by subtracting both sides by 4x (addition property of equality), resulting in 6y=23-4x. To make the y separate from everything else, we divide by 6, resulting in (23-4x) / 6=y. To solve for x, we can do something similar - subtract 6y from both sides to get 23-6y=4x. Next, divide both sides by 4 to get (23-6y) / 4=x.

Since we know that (23-4x) / 6=y, we can plug that into 7y-8x=5, resulting in

7 * (23-4x) / 6-8x=5

= (161-28x) / 6-8x

Multiplying both sides by 6, we get 161-28x-48x=30

= 161-76x

Subtracting 161 from both sides, we get - 131=-76x. Next, we can divide both sides by - 76 to separate the x and get x=131/76. Plugging that into 4x+6y=23, we get 4 (131/76) + 6y=23. Subtracting 4 (131/76) from both sides, we get

6y=23-524/76. Lastly, we can divide both sides by 6 to get y = (23-524/76) / 6

Good luck, and feel free to ask any questions!