1Cademy - Verifying Whether $$(2, -1)$$ and $$(3, 2)$$ are Solutions of $$\{3x - y = 7,\; x

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Solution of a Linear Equation in Two Variables

Example

Verifying Whether $(2, -1)$ and $(3, 2)$ are Solutions of $\{3x - y = 7,\; x - 2y = 4\}$

Consider the system $\left\{\begin{array}{l} 3x - y = 7 \\ x - 2y = 4 \end{array}\right.$

Testing $(2, -1)$ : Substitute $x = 2$ and $y = -1$ into both equations.

First equation: $3(2) - (-1) = 6 + 1 = 7$ . Since $7 = 7$ is true, the first equation is satisfied.
Second equation: $2 - 2(-1) = 2 + 2 = 4$ . Since $4 = 4$ is true, the second equation is also satisfied.

Because both equations produce true statements, $(2, -1)$ is a solution of the system.

Testing $(3, 2)$ : Substitute $x = 3$ and $y = 2$ into both equations.

First equation: $3(3) - 2 = 9 - 2 = 7$ . Since $7 = 7$ is true, the first equation is satisfied.
Second equation: $3 - 2(2) = 3 - 4 = -1$ . Since $-1 \neq 4$ is false, the second equation is not satisfied.

Although $(3, 2)$ satisfies the first equation, it does not satisfy the second. Because it fails to make both equations true, $(3, 2)$ is not a solution of the system.

Updated 2026-04-21

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OpenStax Elementary Algebra

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