Question

Solve the system by substitution

Answer 1

Answer:

The solution to the system of equations be:

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

Step-by-step 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

$\frac{14x}{14}=\frac{42}{14}$

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:

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