Question

question 10 of 10
solve the following system of equation
pair in the format (a,b), with no spaces
2x + 7y = -7
-4x - 3y = -19

Explanation:

Step1: Multiply first equation by 2

To eliminate \(x\), we multiply the first equation \(2x + 7y=-7\) by 2. So we get \(4x + 14y=-14\).

Step2: Add to second equation

Now we add this new equation to the second equation \(-4x - 3y=-19\).
\((4x + 14y)+(-4x - 3y)=-14+(-19)\)
Simplifying the left side: \(4x-4x + 14y-3y = 11y\)
Simplifying the right side: \(-14-19=-33\)
So we have \(11y=-33\).

Step3: Solve for y

Divide both sides of \(11y = -33\) by 11: \(y=\frac{-33}{11}=-3\).

Step4: Substitute y into first equation

Substitute \(y = -3\) into \(2x+7y=-7\): \(2x+7\times(-3)=-7\)
Simplify: \(2x-21=-7\)
Add 21 to both sides: \(2x=-7 + 21=14\)
Divide by 2: \(x=\frac{14}{2}=7\).

Answer:

(7,-3)