Question

solve the following system of equations.
2x - 7y = -11
-7x + 4y = 18
x =

y =

Explanation:

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

Multiply the first equation \(2x - 7y = -11\) by 7: \(14x - 49y = -77\)
Multiply the second equation \(-7x + 4y = 18\) by 2: \(-14x + 8y = 36\)

Step2: Add the two new equations

\((14x - 49y) + (-14x + 8y) = -77 + 36\)
Simplify: \(-41y = -41\)

Step3: Solve for y

Divide both sides by -41: \(y = \frac{-41}{-41} = 1\)

Step4: Substitute y = 1 into the first original equation

\(2x - 7(1) = -11\)
Simplify: \(2x - 7 = -11\)

Step5: Solve for x

Add 7 to both sides: \(2x = -11 + 7 = -4\)
Divide by 2: \(x = \frac{-4}{2} = -2\)

Answer:

\(x = -2\)
\(y = 1\)