Question

solve the following system of equations.
-9x + 4y = 16
-7x + 6y = 24
x =

y =

Explanation:

Step1: Eliminate y by multiplying equations

Multiply the first equation \(-9x + 4y = 16\) by 3: \( -27x + 12y = 48 \)
Multiply the second equation \(-7x + 6y = 24\) by 2: \( -14x + 12y = 48 \)

Step2: Subtract the two new equations

Subtract the second new equation from the first: \((-27x + 12y) - (-14x + 12y) = 48 - 48\)
Simplify: \(-27x + 12y + 14x - 12y = 0\) → \(-13x = 0\) → \(x = 0\)

Step3: Substitute x into first equation

Substitute \(x = 0\) into \(-9x + 4y = 16\): \(-9(0) + 4y = 16\) → \(4y = 16\) → \(y = 4\)

Answer:

\(x = 0\)
\(y = 4\)