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10m+4n=14 5m + n/2 = 14

July 23, 2026Mathematics

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Answer

m = \frac{49}{15}, n = -\frac{14}{3}

3 steps

let's solve this system of equations.

Given equations:

Multiply equation (2) by 2 to eliminate the fraction and make the coefficient of $m$ easier to work with.
$2\left(5m + \frac{n}{2}\right) = 2(14)$ $10m + n = 28 \quad (3)$
Subtract equation (3) from equation (1) to eliminate $m$ .
$(10m + 4n) - (10m + n) = 14 - 28$ $10m + 4n - 10m - n = -14$ $3n = -14$ $n = -\frac{14}{3}$
Substitute the value of $n$ into equation (3) to solve for $m$ .
$10m + \left(-\frac{14}{3}\right) = 28$ $10m - \frac{14}{3} = 28$ $10m = 28 + \frac{14}{3}$ $10m = \frac{28 \times 3}{3} + \frac{14}{3}$ $10m = \frac{84}{3} + \frac{14}{3}$ $10m = \frac{98}{3}$ $m = \frac{98}{3 \times 10}$ $m = \frac{98}{30}$ $m = \frac{49}{15}$
The solution is $m = \frac{49}{15}, n = -\frac{14}{3}$ .

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