Question

find the solution of the system of equations.

\\(-x + 3y = 6\\)
\\(-10x - 3y = 27\\)

Explanation:

Step1: Add the two equations to eliminate \( y \)

The two equations are:
\( -x + 3y = 6 \)
\( -10x - 3y = 27 \)

Adding them together: \((-x + 3y)+(-10x - 3y)=6 + 27\)
Simplify the left side: \(-x-10x+3y - 3y=-11x\)
Simplify the right side: \(33\)
So we get \(-11x = 33\)

Step2: Solve for \( x \)

Divide both sides of \(-11x = 33\) by \(-11\):
\(x=\frac{33}{-11}=- 3\)

Step3: Substitute \( x = - 3 \) into the first equation to find \( y \)

Substitute \( x=-3 \) into \(-x + 3y=6\):
\(-(-3)+3y = 6\)
Simplify: \(3 + 3y=6\)
Subtract 3 from both sides: \(3y=6 - 3=3\)
Divide both sides by 3: \(y = 1\)

Answer:

The solution of the system is \(x=-3,y = 1\) (or in ordered pair form \((-3,1)\))