Answer:
The solution to the system of equations will be:
[tex]y=3,\:x=3[/tex]
Step-by-step explanation:
Given the system of equations
y = x
y = 4x - 9
solving the system of equations by the substitution method
[tex]\begin{bmatrix}y=x\\ y=4x-9\end{bmatrix}[/tex]
substitute y = 4x - 9
[tex]\begin{bmatrix}4x-9=x\end{bmatrix}[/tex]
now isolate x for 4x-9 = x
[tex]4x-9=x[/tex]
Add 9 to both sides
[tex]4x-9+9=x+9[/tex]
Simplify
[tex]4x=x+9[/tex]
Subtract x from both sides
[tex]4x-x=x+9-x[/tex]
Simplify
[tex]3x=9[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=\frac{9}{3}[/tex]
Simplify
[tex]x=3[/tex]
For y=4x-9 substituute x = 3
[tex]y=4\cdot \:3-9[/tex]
Simplify
[tex]y=3[/tex]
Therefore, the solution to the system of equations will be:
[tex]y=3,\:x=3[/tex]
