Question

find the solution of the system of equations,
$-3x + 10y = 2$
$-3x + 3y = 9$

Explanation:

Step1: Subtract the two equations

Subtract the second equation \(-3x + 3y = 9\) from the first equation \(-3x + 10y = 2\) to eliminate \(x\).

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Step2: Solve for \(y\)

Divide both sides of \(7y = -7\) by 7.

$$ y = \frac{-7}{7} = -1 $$

Step3: Substitute \(y\) into one equation

Substitute \(y = -1\) into the second equation \(-3x + 3y = 9\).

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Step4: Solve for \(x\)

Add 3 to both sides: \(-3x = 9 + 3 = 12\). Then divide by -3: \(x = \frac{12}{-3} = -4\).

Answer:

The solution is \(x = -4\), \(y = -1\)