Question

How do you solve the system of equations by using substitution: y = x + 5 and y = 2x - 7?

Answer 1

Solve the first equation for x, substitute into the second equation, and get the answer of `x=12` and `y=17`

Explanation:

To solve using substitution, we'll take one of the equations (the first one - it's a very simple one), solve for x, and then substitute it into the second one.

So let's first take `y=x+5` and solve for `x`:

`y=x+5` - subtract 5 from both sides and we get

`y-5=x`

And now we can substitute that into the 2nd equation:

`y=2x-7`
`y=2(y-5)-7`

and let's simplify

`y=2y-10-7` - we can subtract `2y` from both sides and combine terms
`-y=-17`
`y=17`

We can now substitute the y value back into the given equations and find the x value:

`y=x+5`
`17=x+5`
`x=12`

`y=2x-7`
`17=2x-7`
`24=2x`
`x=12`

And we're done! `x=12` and `y=17`