EDGE Math 8

Example 2

Solve the given system of linear equations using the elimination method. Find out what type of system of equations it is.

{\begin{array}{l} 2 x - y = - 2 \\ - 2 x + 3 y = 6 \end{array}

Solution

The coefficients of x in the first and second equations (which are 2 and −2, respectively) are additive inverses. Add the first equation to the second equation.

\begin{array}{l} 2 x - y = - 2 \\ \underline{+ - 2 x + 3 y = 6} \\ 2 y = 4 \end{array}

Then solve for y.

$2 y$	$= 4$
$y$	$= \frac{4}{2}$
$y$	$= 2$

To solve for x, substitute 2 for y in either the first or the second equation of the given system. Substituting 2 for y in the first equation results in the following:

$2 x - 2$	$= - 2$
$2 x$	$= - 2 + 2$
$2 x$	$= 0$
$x$	$= \frac{0}{2}$
$x$	$= 0.$

The solution of the given system is $(0, 2) .$ The system is consistent and independent. As an exercise, substitute 0 for x and 2 for y in both equations and show that the equations are satisfied.

Elimination Method