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Solve the system of linear equations: 3x + 2y = 8 and 2x − y = 3.

May 10, 2026Mathematics

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Answer

x=2, y=1

6 steps

Identify the system of equations.
The given system of equations is:
$3x + 2y = 8 \quad \text{(1)}$ $2x - y = 3 \quad \text{(2)}$
Multiply equation (2) by 2 to make the coefficients of $y$ opposites.
$2(2x - y) = 2(3)$ $4x - 2y = 6 \quad \text{(3)}$
Add equation (1) and equation (3) to eliminate $y$ .
$(3x + 2y) + (4x - 2y) = 8 + 6$ $3x + 4x + 2y - 2y = 14$ $7x = 14$
Solve for $x$ .
$x = \frac{14}{7}$ $x = 2$
Substitute the value of $x$ into equation (2) to solve for $y$ .
$2(2) - y = 3$ $4 - y = 3$
Solve for $y$ .
$-y = 3 - 4$ $-y = -1$ $y = 1$
The solution to the system of equations is:
$x=2, y=1$

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