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Solve the following system of equations: x + 3y = 6 and −x + 8y = 5

May 10, 2026Mathematics

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Answer

x=3, y=1

5 steps

Identify the system of equations.
The given system of equations is:
$x + 3y = 6 \quad \text{(1)}$ $-x + 8y = 5 \quad \text{(2)}$
Add equation (1) and equation (2) to eliminate $x$ .
$(x + 3y) + (-x + 8y) = 6 + 5$ $x - x + 3y + 8y = 11$ $11y = 11$
Solve for $y$ .
$y = \frac{11}{11}$ $y = 1$
Substitute the value of $y$ into equation (1) to solve for $x$ .
$x + 3(1) = 6$ $x + 3 = 6$
Solve for $x$ .
$x = 6 - 3$ $x = 3$
The solution to the system of equations is:
$x=3, y=1$

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