Answer
$\left (\frac{2}{3},1 \right)$.
Work Step by Step
The given system of equations is
$\Rightarrow y=3-3x$ ...... (1)
$\Rightarrow 3x+4y=6$ ...... (2)
Substitute the value of $y$ from equation (1) to equation (2).
$\Rightarrow 3x+4(3-3x)=6$
Simplify.
$\Rightarrow 3x+12-12x=6$
Add like terms.
$\Rightarrow 12-9x=6$
Subtract $12$ from both sides.
$\Rightarrow 12-9x-12=6-12$
Simplify.
$\Rightarrow -9x=-6$
Divide both sides by $-9$.
$\Rightarrow \frac{-9x}{-9}=\frac{-6}{-9}$
Simplify.
$\Rightarrow x=\frac{2}{3}$
Plug the value of $x$ into equation (1).
$\Rightarrow y=3-3\left( \frac{2}{3}\right)$
Cancel common terms.
$\Rightarrow y=3-2$
Add like terms.
$\Rightarrow y=1$
To check solution plug $\left (\frac{2}{3},1 \right)$ into equation (2).
$\Rightarrow 3\left( \frac{2}{3}\right)+4(1)=6$
$\Rightarrow 2+4=6$
$\Rightarrow 6=6$ True.
Hence, the solution set is $\left (\frac{2}{3},1 \right)$.
