Question

1. solve by substitution: \

$$\begin{cases} 6x - 3y = -33 \\\\ 2x + y = -1 \\end{cases}$$

Explanation:

Step1: Solve for y from the second equation

From \(2x + y = -1\), we can express \(y\) as \(y=-1 - 2x\).

Step2: Substitute y into the first equation

Substitute \(y = -1 - 2x\) into \(6x-3y=-33\). We get \(6x-3(-1 - 2x)=-33\).

Step3: Simplify and solve for x

First, expand the left - hand side: \(6x + 3+6x=-33\). Combine like terms: \(12x+3=-33\). Subtract 3 from both sides: \(12x=-33 - 3=-36\). Then divide both sides by 12: \(x=\frac{-36}{12}=-3\).

Step4: Substitute x back to find y

Substitute \(x = -3\) into \(y=-1 - 2x\). Then \(y=-1-2\times(-3)=-1 + 6 = 5\).

Answer:

The solution of the system of equations is \(x=-3,y = 5\) (or the ordered pair \((-3,5)\))