Question

-4x - 2y = 14
-10x + 7y = -25

Explanation:

Step1: Eliminate a variable (e.g., y)

First, multiply the first equation \(-4x - 2y = 14\) by 7 and the second equation \(-10x + 7y = -25\) by 2 to make the coefficients of y opposite.
For the first equation: \(7\times(-4x - 2y)=7\times14\) gives \(-28x - 14y = 98\).
For the second equation: \(2\times(-10x + 7y)=2\times(-25)\) gives \(-20x + 14y = -50\).

Step2: Add the two new equations

\((-28x - 14y)+(-20x + 14y)=98+(-50)\)
Simplify: \(-48x = 48\)

Step3: Solve for x

Divide both sides by -48: \(x=\frac{48}{-48}=-1\)

Step4: Substitute x into one of the original equations (e.g., first equation)

Substitute \(x = -1\) into \(-4x - 2y = 14\):
\(-4\times(-1)-2y = 14\)
Simplify: \(4 - 2y = 14\)
Subtract 4 from both sides: \(-2y = 14 - 4 = 10\)
Divide by -2: \(y=\frac{10}{-2}=-5\)

Answer:

\(x = -1\), \(y = -5\)