# Solve the system of equations.-3x-y=-10 ; 4x-4y=8

## Question:

Solve the system of equations.

{eq}-3x - y= -10 ; \, {/eq} {eq}4x - 4y = 8 {/eq}

## System of Linear Equations:

The system of linear equations constitutes a number of linear equations (two or more than two), which are solved by eliminating the variables one by one. By applying substitution method, the value of other variables is determined.

Write the system of equations.

\begin{align*} - 3x - y &= - 10................(I)\\[0.3cm] 4x - 4y &= 8....................(II) \end{align*}

Solving for {eq}y{/eq} in equation (I)

$$y = - 3x + 10$$

Substitute {eq}- 3x + 10{/eq} for {eq}y{/eq} in Equation (II)

\begin{align*} 4x - 4\left( { - 3x + 10} \right) &= 8\\[0.3cm] 4x + 12x - 40 &= 8\\[0.3cm] 16x - 40 &= 8\\[0.3cm] 16x &= 40 + 8\\[0.3cm] 16x &= 48\\[0.3cm] x &= \dfrac{{48}}{{16}}\\[0.3cm] &= 3 \end{align*}

Substitute {eq}3{/eq} for {eq}x{/eq} in the equation (I)

\begin{align*} y &= - 3 \times 3 + 10\\[0.3cm] &= - 9 + 10\\[0.3cm] &= 1 \end{align*}

Thus, the value for {eq}x {/eq} is {eq}3 {/eq} and the value for {eq}y {/eq} is {eq}1 {/eq}.