Question

Solve the system of equations by using substitution.
x+8y=-2
x-3y=20

Answer 1

(14, -2)

Explanation:

To solve by using substitution, begin by solving for a variable in the first equation. Let's solve for x:

`x+8y=-2\\x=-2-8y`

Now we know what x equals. Let's substitute this into the second equation:

`x-3y=20\\(-2-8y)-3y=20`

We can then simplify:

`-2-8y-3y=20` Given equation

`-2-11y=20` Combine y terms

`-11y=22` Add 2

`y=-2` Divide by -11

So, we now know the value of y = -2.

To find the value of X, we can substitute the value of Y into one of the equations. Let's use the first one:

`x+8y=-2`

`x+8(-2)=-2` Substitute for y

`x-16=-2` Distribute 8

`x=14` Add 16

So, we now know the value of x = 14.

Therefore, we know a solution to the system of equations is (14, -2).