1Cademy - Solving $$\left\{4x + y = -5,\; -2x - 2y = -2\right\}$$ by Elimination

Learn Before

Solving a System of Linear Equations by Elimination

Example

Solving $\left\{4x + y = -5,\; -2x - 2y = -2\right\}$ by Elimination

Solve the system $\left\{\begin{array}{l} 4x + y = -5 \\ -2x - 2y = -2 \end{array}\right.$ using the elimination method.

Step 1 — Write both equations in standard form. Both equations are already in the standard form $Ax + By = C$ .

Step 2 — Make the coefficients of one variable opposites. To eliminate $y$ , multiply the first equation by $2$ so that the $y$ -coefficients become $2$ and $-2$ :

$2(4x + y) = 2(-5) \implies 8x + 2y = -10$

The system becomes $\left\{\begin{array}{l} 8x + 2y = -10 \\ -2x - 2y = -2 \end{array}\right.$

Step 3 — Add the equations to eliminate one variable. Adding the left and right sides together:

$8x + 2y - 2x - 2y = -10 - 2$

$6x = -12$

The $y$ -terms cancel because $2y + (-2y) = 0$ .

Step 4 — Solve for the remaining variable. Divide both sides by $6$ :

$x = -2$

Step 5 — Substitute back into an original equation. Substitute $x = -2$ into the first original equation $4x + y = -5$ :

$4(-2) + y = -5$

$-8 + y = -5$

$y = 3$

Step 6 — Write the solution as an ordered pair: $(-2, 3)$ .

Step 7 — Check in both original equations:

First equation: $4(-2) + 3 = -8 + 3 = -5$ . Since $-5 = -5$ is true ✓
Second equation: $-2(-2) - 2(3) = 4 - 6 = -2$ . Since $-2 = -2$ is true ✓

Because both equations are satisfied, the solution of the system is $(-2, 3)$ .

Updated 2026-05-07

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related