Question

solve the following system of equations.
-3x + 5y = 23
2x + 3y = 10
x =

y =

Explanation:

Step1: Eliminate x by scaling equations

Multiply the first equation \(-3x + 5y = 23\) by 2: \( -6x + 10y = 46 \).
Multiply the second equation \(2x + 3y = 10\) by 3: \( 6x + 9y = 30 \).

Step2: Add the scaled equations

Add \(-6x + 10y = 46\) and \(6x + 9y = 30\):
\((-6x + 6x) + (10y + 9y) = 46 + 30\)
\(19y = 76\)

Step3: Solve for y

Divide both sides by 19: \( y = \frac{76}{19} = 4 \).

Step4: Substitute y into an equation

Substitute \(y = 4\) into \(2x + 3y = 10\):
\(2x + 3(4) = 10\)
\(2x + 12 = 10\)

Step5: Solve for x

Subtract 12: \(2x = 10 - 12 = -2\)
Divide by 2: \(x = \frac{-2}{2} = -1\).

Answer:

\( x = -1 \)
\( y = 4 \)