<p>The elimination method removes one unknown by adding or subtracting the two equations. Either \(x\) or \(y\) may be eliminated first.</p>
<ol class="num-list"><li data-list-item-id="elim-s1" data-list-item-path="elim-s1"><div class="list-item-paragraph">Choose the unknown to eliminate. Compare the numerical values and signs of its coefficients.</div></li><li data-list-item-id="elim-s2" data-list-item-path="elim-s2"><div class="list-item-paragraph">If the coefficient magnitudes are different, multiply one or both equations by suitable numbers so that they become equal. The LCM of the coefficients is often useful.</div></li><li data-list-item-id="elim-s3" data-list-item-path="elim-s3"><div class="list-item-paragraph">When the equal coefficients have the same sign, subtract the equations. When they have opposite signs, add the equations.</div></li><li data-list-item-id="elim-s4" data-list-item-path="elim-s4"><div class="list-item-paragraph">Solve the resulting linear equation in one unknown.</div></li><li data-list-item-id="elim-s5" data-list-item-path="elim-s5"><div class="list-item-paragraph">Substitute the value obtained into either original equation to find the other unknown.</div></li><li data-list-item-id="elim-s6" data-list-item-path="elim-s6"><div class="list-item-paragraph">Check both values in the two original equations. Ensure that&nbsp;\(\text{LHS}=\text{RHS}\) for each equation.</div></li></ol>
<p>State the solution as the ordered pair \((x,y)\).</p>

The elimination method removes one unknown by adding or subtracting the two equations. Either \(x\) or \(y\) may be eliminated first.

Choose the unknown to eliminate. Compare the numerical values and signs of its coefficients.

If the coefficient magnitudes are different, multiply one or both equations by suitable numbers so that they become equal. The LCM of the coefficients is often useful.

When the equal coefficients have the same sign, subtract the equations. When they have opposite signs, add the equations.

Solve the resulting linear equation in one unknown.

Substitute the value obtained into either original equation to find the other unknown.

Check both values in the two original equations. Ensure that \(\text{LHS}=\text{RHS}\) for each equation.

Elimination Method

Elimination Method