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Solve the system of linear equations: 3x − 2y = 19 and 5x + 2y = 21.

April 16, 2026Mathematics

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Answer

x=5, y=-2

4 steps

Here are the given equations:

3x - 2y = 19 \quad (1)

5x + 2y = 21 \quad (2)

Add equation (1) and equation (2) to eliminate $y$ .
$(3x - 2y) + (5x + 2y) = 19 + 21$ $3x + 5x - 2y + 2y = 40$ $8x = 40$
Solve for $x$ .
$\frac{8x}{8} = \frac{40}{8}$ $x = 5$
Substitute the value of $x = 5$ into equation (1).
$3(5) - 2y = 19$ $15 - 2y = 19$
Solve for $y$ .
$-2y = 19 - 15$ $-2y = 4$ $\frac{-2y}{-2} = \frac{4}{-2}$ $y = -2$
The solution is $x=5$ and $y=-2$ .
$x=5, y=-2$

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