Question

solve the following system of equations.
-4x + 7y = 19
-3x - 5y = 4
x =

y =

Explanation:

Step1: Eliminate x by scaling equations

Multiply first equation by 3: \(3(-4x + 7y)=3(19)\) → \(-12x + 21y = 57\)
Multiply second equation by 4: \(4(-3x - 5y)=4(4)\) → \(-12x - 20y = 16\)

Step2: Subtract equations to solve for y

Subtract the second new equation from the first:
\((-12x + 21y) - (-12x - 20y) = 57 - 16\)
Simplify: \(41y = 41\) → \(y = 1\)

Step3: Substitute y into an original equation

Use \(-4x + 7y = 19\), substitute \(y = 1\):
\(-4x + 7(1) = 19\) → \(-4x + 7 = 19\)
Subtract 7: \(-4x = 12\) → \(x = -3\)

Answer:

\(x = -3\), \(y = 1\)