Question

solve using elimination.
6x - 10y = 16
8x - 7y = 15
(□, □)
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Explanation:

Step1: Make coefficients of x opposites

Multiply first equation by 4: \(4(6x - 10y)=4\times16\) → \(24x - 40y = 64\)
Multiply second equation by -3: \(-3(8x - 7y)=-3\times15\) → \(-24x + 21y = -45\)

Step2: Add equations to eliminate x

\((24x - 40y)+(-24x + 21y)=64 + (-45)\)
\(24x - 24x - 40y + 21y = 19\) → \(-19y = 19\)

Step3: Solve for y

Divide by -19: \(y=\frac{19}{-19}=-1\)

Step4: Substitute y into first equation

\(6x - 10(-1)=16\) → \(6x + 10 = 16\)
Subtract 10: \(6x = 6\)
Divide by 6: \(x = 1\)

Answer:

\((1, -1)\)