Question

Use substitution to solve the system of linear equations. In your final answer, include all of your work.

Answer 1

The solution is $(1,1)$

Step-by-step explanation:

The system of linear equation is

$y=-3x+4$ and $y+\frac{1}{3} y=\frac{4}{3}$

Using substitution method, let us substitute $y=-3x+4$ in the equation

$y+\frac{1}{3} y=\frac{4}{3}$

$-3 x+4+\frac{1}{3}(-3 x+4)=\frac{4}{3}$

Multiplying the term $-3x+4$ by $\frac{1}{3}$, we get,

$-3 x+4-x+\frac{4}{3}=\frac{4}{3}$

Subtracting both sides by $\frac{4}{3}$,

$-3x+4-x=0$

Simplifying, we get,

$\begin{aligned}-4 x+4 &=0 \\-4 x &=-4 \\x &=1\end{aligned}$

Now, substitute $x=1$ in $y=-3x+4$

$y=-3(1)+4\\y=-3+4\\y=1$

Thus, the solution is $(1,1)$