Answer:
The solution to the system of equations be:
[tex]x=3,\:y=-2[/tex]
Step-by-step explanation:
Given the system of equations
4x-2y = 16
y = -5x+13
Solving the system of equations using the substitution method
[tex]\begin{bmatrix}4x-2y=16\\ y=-5x+13\end{bmatrix}[/tex]
Substitute y = -5x+13 in 4x-2y = 16
[tex]4x-2\left(-5x+13\right)=16[/tex]
[tex]4x+10x-26 = 16[/tex]
[tex]14x-26 = 16[/tex]
Now isolate x for [tex]14x-26 = 16[/tex]
[tex]14x-26=16[/tex]
Add 26 to both sides
[tex]14x-26+26=16+26[/tex]
Simplify
[tex]14x=42[/tex]
Divide both sides by 14
[tex]\frac{14x}{14}=\frac{42}{14}[/tex]
Simplify
[tex]x=3[/tex]
For y = -5x+13
Substitute x = 3
[tex]y=-5\cdot \:3+13[/tex]
Simplify
[tex]y=-2[/tex]
Therefore, the solution to the system of equations be:
[tex]x=3,\:y=-2[/tex]
