Question

solve the following system of equations. -5x - 6y = 15 7x + 3y = -21 x = \square y = \square

Explanation:

Step1: Eliminate y by multiplying the second equation

Multiply the second equation \(7x + 3y=-21\) by 2 to get \(14x + 6y=-42\).

Step2: Add the two equations

Add the first equation \(-5x - 6y = 15\) and the new second equation \(14x + 6y=-42\). So, \((-5x+14x)+(-6y + 6y)=15+(-42)\), which simplifies to \(9x=-27\).

Step3: Solve for x

Divide both sides of \(9x=-27\) by 9: \(x=\frac{-27}{9}=-3\).

Step4: Substitute x into one of the original equations

Substitute \(x = - 3\) into the second equation \(7x+3y=-21\). We get \(7\times(-3)+3y=-21\), which is \(-21 + 3y=-21\).

Step5: Solve for y

Add 21 to both sides: \(3y=-21 + 21=0\), then divide by 3: \(y = 0\).

Answer:

\(x=-3\)
\(y = 0\)