1Cademy - Solving $$\{3x + y = -1,\; 2x + y = 0\}$$ by Graphing

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Solving a System of Linear Equations by Graphing

Example

Solving $\{3x + y = -1,\; 2x + y = 0\}$ by Graphing

Solve the system $\left\{\begin{array}{l} 3x + y = -1 \\ 2x + y = 0 \end{array}\right.$ using the graphing method.

Because both equations are in standard form, first rewrite each one in slope-intercept form by isolating $y$ .

First equation: $3x + y = -1$ becomes $y = -3x - 1$ . The slope is $m = -3$ and the y-intercept is $(0, -1)$ .

Second equation: $2x + y = 0$ becomes $y = -2x$ . The slope is $m = -2$ and the y-intercept is $(0, 0)$ .

Graph both lines on the same coordinate system using their slopes and y-intercepts. The two lines cross at the point $(-1, 2)$ .

Verify the solution by substituting $x = -1$ and $y = 2$ into both original equations:

First equation: $3(-1) + 2 = -3 + 2 = -1$ . Since $-1 = -1$ is true ✓
Second equation: $2(-1) + 2 = -2 + 2 = 0$ . Since $0 = 0$ is true ✓

Because $(-1, 2)$ satisfies both equations, the solution of the system is $(-1, 2)$ .

This example illustrates that when both equations in a system are given in standard form, solving each for $y$ converts them to slope-intercept form so the lines can be graphed using their slopes and y-intercepts.

Updated 2026-04-24

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