Question

solve the following system of equations.
$5x + 6y = 23$
$4x + 7y = 14$
$x = \square$
$y = \square$

Explanation:

Step1: Eliminate x by multiplying equations

Multiply the first equation \(5x + 6y = 23\) by 4: \(20x + 24y = 92\)
Multiply the second equation \(4x + 7y = 14\) by 5: \(20x + 35y = 70\)

Step2: Subtract the two new equations

Subtract the first new equation from the second:
\((20x + 35y) - (20x + 24y) = 70 - 92\)
\(11y = -22\)

Step3: Solve for y

Divide both sides by 11: \(y = \frac{-22}{11} = -2\)

Step4: Substitute y into one of the original equations

Substitute \(y = -2\) into \(5x + 6y = 23\):
\(5x + 6(-2) = 23\)
\(5x - 12 = 23\)

Step5: Solve for x

Add 12 to both sides: \(5x = 35\)
Divide by 5: \(x = 7\)

Answer:

\(x = 7\)
\(y = -2\)