Question

solve the following system of equations.
-5x + 6y = -3
4x - 5y = 1
x =

y =

Explanation:

Step1: Multiply equations to eliminate a variable

Multiply the first equation \(-5x + 6y = -3\) by \(4\) and the second equation \(4x - 5y = 1\) by \(5\) to make the coefficients of \(x\) opposites.
First equation: \(4(-5x + 6y) = 4(-3)\) → \(-20x + 24y = -12\)
Second equation: \(5(4x - 5y) = 5(1)\) → \(20x - 25y = 5\)

Step2: Add the two new equations

Add \(-20x + 24y = -12\) and \(20x - 25y = 5\) to eliminate \(x\):
\((-20x + 20x) + (24y - 25y) = -12 + 5\)
\(-y = -7\)

Step3: Solve for \(y\)

Multiply both sides by \(-1\): \(y = 7\)

Step4: Substitute \(y = 7\) into one of the original equations

Substitute \(y = 7\) into \(4x - 5y = 1\):
\(4x - 5(7) = 1\)
\(4x - 35 = 1\)

Step5: Solve for \(x\)

Add \(35\) to both sides: \(4x = 36\)
Divide by \(4\): \(x = 9\)

Answer:

\(x = 9\), \(y = 7\)