Question

1. \

$$\begin{cases} x - 2y = 10 \\\\ x + 3y = 5 \\end{cases}$$

1. \

$$\begin{cases} 2x - \\\\ -5x \\end{cases}$$

Explanation:

Step1: Subtract the two equations

We have the system of equations:

$$
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$$

Subtract equation \((1)\) from equation \((2)\): \((x + 3y)-(x - 2y)=5 - 10\)
Simplify the left - hand side: \(x+3y - x + 2y=5y\)
Simplify the right - hand side: \(5-10=-5\)
So we get the equation \(5y=-5\)

Step2: Solve for y

From \(5y=-5\), divide both sides by 5: \(y=\frac{-5}{5}=-1\)

Step3: Substitute y into one of the original equations

Substitute \(y = - 1\) into equation \((1)\): \(x-2\times(-1)=10\)
Simplify the left - hand side: \(x + 2=10\)
Subtract 2 from both sides: \(x=10 - 2=8\)

Answer:

The solution of the system of equations is \(x = 8,y=-1\)