Question

solve the following system.
\\(\

$$\begin{cases}4x - 3y = 4\\x=-2\\-3x + 2y - z=-7\\end{cases}$$

\\)

Explanation:

Step1: Substitute x into first - equation

Given $x = - 2$, substitute into $4x-3y = 4$. We get $4\times(-2)-3y = 4$, which simplifies to $-8 - 3y=4$.

Step2: Solve for y

Add 8 to both sides of $-8 - 3y=4$: $-3y=4 + 8=12$. Then divide both sides by - 3, so $y=\frac{12}{-3}=-4$.

Step3: Substitute x and y into third - equation

Substitute $x=-2$ and $y = - 4$ into $-3x + 2y-z=-7$. We have $-3\times(-2)+2\times(-4)-z=-7$.

Step4: Simplify the left - hand side

Calculate $-3\times(-2)+2\times(-4)-z$: $6-8 - z=-7$. Combine like - terms: $-2 - z=-7$.

Step5: Solve for z

Add 2 to both sides of $-2 - z=-7$, we get $-z=-7 + 2=-5$. Multiply both sides by - 1, so $z = 5$.

Answer:

$x=-2$, $y=-4$, $z = 5$