Question

1. solve the system

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

Explanation:

Step1: Solve the second equation for y

From \(-5x + y = 3\), we can express \(y\) in terms of \(x\) by adding \(5x\) to both sides. So, \(y = 5x + 3\).

Step2: Substitute y into the first equation

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

Step3: Simplify and solve for x

First, expand the left - hand side: \(3x-10x - 6=-4\).
Combine like terms: \(-7x-6 = - 4\).
Add 6 to both sides: \(-7x=-4 + 6=2\).
Divide both sides by \(-7\): \(x=-\frac{2}{7}\).

Step4: Substitute x back to find y

Substitute \(x = -\frac{2}{7}\) into \(y = 5x+3\). Then \(y=5\times(-\frac{2}{7})+3=-\frac{10}{7}+\frac{21}{7}=\frac{11}{7}\).

Answer:

The solution to the system of equations is \(x = -\frac{2}{7}\) and \(y=\frac{11}{7}\)