Question

question
solve the system of equations using elimination: -x + y = -10 and 3x + 4y = -19.
answer attempt 1 out of 2
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Explanation:

Step1: Multiply first equation by 3

To eliminate \(x\), multiply the first equation \(-x + y=-10\) by 3. We get \(3\times(-x + y)=3\times(-10)\), which simplifies to \(-3x + 3y=-30\).

Step2: Add to second equation

Now add this new equation \(-3x + 3y=-30\) to the second equation \(3x + 4y=-19\).

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Step3: Solve for \(y\)

Divide both sides of \(7y = - 49\) by 7: \(y=\frac{-49}{7}=-7\).

Step4: Substitute \(y\) into first equation

Substitute \(y = - 7\) into the first equation \(-x + y=-10\). We have \(-x+(-7)=-10\).

Step5: Solve for \(x\)

Simplify the equation: \(-x-7=-10\). Add 7 to both sides: \(-x=-10 + 7=-3\). Multiply both sides by - 1: \(x = 3\).

Answer:

\((3,-7)\)