Question

I just need help explaining it. solve the system of equation

Answer 1

SOLUTION

Write out the equation

$\begin{gathered} y=\frac{1}{3}x-3 \\ 5x-3y=-3 \end{gathered}$

To solve this system of equation, the aprropriate method will be substitution

Substitute the expression for y into the second equation for y, we have

$5x-3(\frac{1}{3}x-3)=-3$

Expand the paranthesis we have

$\begin{gathered} 5x-x+9=-3 \\ \text{Simplify},\text{ by subtracting 9 from both sides } \\ 4x+9-9=-3-9 \\ 4x=-12 \end{gathered}$

Divide both sides by 4, we have

$\begin{gathered} \frac{4x}{4}=-\frac{12}{4} \\ \text{Then} \\ x=-3 \end{gathered}$

Since the value of x has been obtained, we substitute into the first equation

$\begin{gathered} y=\frac{1}{3}x-3 \\ \text{ recall x=}-3 \\ y=\frac{1}{3}(-3)-3 \\ y=-1-4 \\ \text{Hence } \\ y=-4 \end{gathered}$

Therefore

x = -3, y= -4