Question

-3x + 5y = -19
2x + y = 4

Explanation:

Step1: Solve the second equation for y

From \(2x + y = 4\), we can express \(y\) in terms of \(x\) as \(y = 4 - 2x\).

Step2: Substitute y into the first equation

Substitute \(y = 4 - 2x\) into \(-3x + 5y = -19\). So we get \(-3x + 5(4 - 2x) = -19\).

Step3: Simplify and solve for x

Expand the equation: \(-3x + 20 - 10x = -19\). Combine like terms: \(-13x + 20 = -19\). Subtract 20 from both sides: \(-13x = -19 - 20=-39\). Divide both sides by -13: \(x=\frac{-39}{-13} = 3\).

Step4: Find y using x = 3

Substitute \(x = 3\) into \(y = 4 - 2x\), we get \(y = 4 - 2\times3 = 4 - 6=-2\).

Answer:

The solution to the system of equations is \(x = 3\) and \(y = -2\)