# Evaluate: {\text{begin}array l 2y+x=4 } y-3x=2\text{end}array .

## Expression: $\left\{\begin{array} { l } 2y+x=4 \\ y-3x=2\end{array} \right.$

Use the commutative property to reorder the terms

$\left\{\begin{array} { l } x+2y=4 \\ y-3x=2\end{array} \right.$

Use the commutative property to reorder the terms

$\left\{\begin{array} { l } x+2y=4 \\ -3x+y=2\end{array} \right.$

Multiply both sides of the equation by $3$

$\left\{\begin{array} { l } 3x+6y=12 \\ -3x+y=2\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$7y=14$

Divide both sides of the equation by $7$

$y=2$

Substitute the given value of $y$ into the equation $-3x+y=2$

$-3x+2=2$

Solve the equation for $x$

$x=0$

The possible solution of the system is the ordered pair $\left( x, y\right)$

$\left( x, y\right)=\left( 0, 2\right)$

Check if the given ordered pair is the solution of the system of equations

$\left\{\begin{array} { l } 2 \times 2+0=4 \\ 2-3 \times 0=2\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 4=4 \\ 2=2\end{array} \right.$

Since all of the equalities are true, the ordered pair is the solution of the system

$\left( x, y\right)=\left( 0, 2\right)$

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