Question

solve the system of equations.
2x - 3y = 1
4x - 5y = 5
x =

y =

submit

Explanation:

Step1: Eliminate x by multiplying first equation

Multiply the first equation \(2x - 3y = 1\) by 2: \(4x - 6y = 2\)

Step2: Subtract the new equation from the second

Subtract \(4x - 6y = 2\) from \(4x - 5y = 5\): \((4x - 5y)-(4x - 6y)=5 - 2\)
Simplify: \(4x - 5y - 4x + 6y = 3\) → \(y = 3\)

Step3: Substitute y into first equation

Substitute \(y = 3\) into \(2x - 3y = 1\): \(2x - 3(3)=1\)
Simplify: \(2x - 9 = 1\) → \(2x = 10\) → \(x = 5\)

Answer:

\(x = 5\), \(y = 3\)