Question

-Solve this system of equations using the substitution method.y = 5x - 3y = -6x + 8Because both equations equal y, we can substitute one of theequations forh). This will create an equation with only one variable, X.5x – 3 = -6x + 8[?]x – 3 = 8Hint: First add 6x to each side of the equation.

Answer 1

Given the system of equations:

$\begin{cases}y={5x-3} \\ y={-6x+8}\end{cases}$

We solve it using the substitution method, then:

$5x-3=-6x+8$

We add 6x on both sides of the equation:

$\begin{gathered} 5x-3+6x=-6x+8+6x \\ 11x-3=8 \end{gathered}$

Now, we add 3 on both sides:

$\begin{gathered} 11x-3+3=8+3 \\ 11x=11 \end{gathered}$

Finally, we divide by 11 on both sides:

$\begin{gathered} \frac{11x}{11}=\frac{11}{11} \\ \\ \therefore x=1 \end{gathered}$

And the solution is:

$\begin{gathered} x=1 \\ y=2 \end{gathered}$