Question

Solve the system by substitution

Answer 1

The solution to the system of equations be:

`x=3,\:y=-2`

Explanation:

Given the system of equations

4x-2y = 16

y = -5x+13

Solving the system of equations using the substitution method

`\begin{bmatrix}4x-2y=16\\ y=-5x+13\end{bmatrix}`

Substitute y = -5x+13 in 4x-2y = 16

`4x-2\left(-5x+13\right)=16`

`4x+10x-26 = 16`

`14x-26 = 16`

Now isolate x for
`14x-26 = 16`

`14x-26=16`

Add 26 to both sides

`14x-26+26=16+26`

Simplify

`14x=42`

Divide both sides by 14

`(14x)/(14)=(42)/(14)`

Simplify

`x=3`

For y = -5x+13

Substitute x = 3

`y=-5\cdot \:3+13`

Simplify

`y=-2`

Therefore, the solution to the system of equations be:

`x=3,\:y=-2`