Answer
The solution is $(2,0)$.
Work Step by Step
The given system of equations is
$\Rightarrow 2x+3y=4$ ...... (1)
$\Rightarrow y+3x=6$ ...... (2)
Subtract $3x$ from each side of equation (2).
$\Rightarrow y+3x-3x=6-3x$
$\Rightarrow y=6-3x$ ...... (3)
Substitute $6-3x$ for $y$ in equation (1).
$\Rightarrow 2x+3(6-3x)=4$
Use distributive property.
$\Rightarrow 2x+18-9x=4$
Add like terms.
$\Rightarrow 18-7x=4$
Add $7x-4$ to each side.
$\Rightarrow 18-7x+7x-4=4+7x-4$
Simplify.
$\Rightarrow 14=7x$
Divide each side by $7$.
$\Rightarrow \frac{14}{7}=\frac{7x}{7}$
Simplify.
$\Rightarrow 2=x$
Substitute $2$ for $x$ in equation (2).
$\Rightarrow y+3(2)=6$
Simplify.
$\Rightarrow y+6=6$
Subtract $6$ from each side.
$\Rightarrow y+6-6=6-6$
Simplify.
$\Rightarrow y=0$
Check $(x,y)=(2,0)$
Equation (1)
$\Rightarrow 2x+3y=4$
$\Rightarrow 2(2)+4(0)=4$
$\Rightarrow 4+0=4$
$\Rightarrow 4=4$
True.
Equation (2)
$\Rightarrow y+3x=6$
$\Rightarrow 0+3(2)=6$
$\Rightarrow 0+6=6$
$\Rightarrow 6=6$
True.
Hence, the solution is $(2,0)$.
