Solve Systems of Equations by Elimination: example 5.26

Solve the system by elimination. ${\begin{matrix} x + y = 10 \\ x - y = 12 \end{matrix}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the system by elimination. ${\begin{matrix} 2 x + y = 5 \\ x - y = 4 \end{matrix}$

How did it go?


Both equations are in standard form.
The coefficients of y are already opposites.
Add the two equations to eliminate y. The resulting equation has only 1 variable, x.
Solve for x, the remaining variable. Substitute x = 11 into one of the original equations.

Solve for the other variable, y.
Write the solution as an ordered pair.	The ordered pair is (11, −1).
Check that the ordered pair is a solution to both original equations. $\begin{matrix} \begin{matrix} x + y & = & 10 \\ 11 + (- 1) & \overset{?}{=} & 10 \\ 10 & = & 10 ✓ \end{matrix} & \begin{matrix} x - y & = & 12 \\ 11 - (- 1) & \overset{?}{=} & 12 \\ 12 & = & 12 ✓ \end{matrix} \end{matrix}$
	The solution is (11, −1).


Both equations are in standard form.
The coefficients of y are already opposites.
Add the two equations to eliminate y. The resulting equation has only 1 variable, x.
Solve for x, the remaining variable. Substitute x = 11 into one of the original equations.

Solve for the other variable, y.
Write the solution as an ordered pair.	The ordered pair is (11, −1).
Check that the ordered pair is a solution to both original equations. $\begin{matrix} \begin{matrix} x + y & = & 10 \\ 11 + (- 1) & \overset{?}{=} & 10 \\ 10 & = & 10 ✓ \end{matrix} & \begin{matrix} x - y & = & 12 \\ 11 - (- 1) & \overset{?}{=} & 12 \\ 12 & = & 12 ✓ \end{matrix} \end{matrix}$
	The solution is (11, −1).