Question

1. -x + 2y = 3

4x - 5y = -3

Explanation:

Step1: Rewrite the system of equations

We have the system:

$$
LATEXBLOCK0
$$

From the first equation, solve for \(x\):
\(-x=3 - 2y\), so \(x = 2y - 3\)

Step2: Substitute \(x\) into the second equation

Substitute \(x = 2y - 3\) into \(4x-5y=-3\):
\(4(2y - 3)-5y=-3\)
Expand the left - hand side: \(8y-12 - 5y=-3\)
Combine like terms: \(3y-12=-3\)

Step3: Solve for \(y\)

Add 12 to both sides of the equation \(3y-12=-3\):
\(3y=-3 + 12=9\)
Divide both sides by 3: \(y = 3\)

Step4: Solve for \(x\)

Substitute \(y = 3\) into \(x = 2y - 3\):
\(x=2\times3-3=6 - 3=3\)

Answer:

The solution of the system of equations is \(x = 3,y = 3\)