Question

1. \\(\

$$\begin{cases}6x - 3y = 12\\\\4x - 3y = 24\\end{cases}$$

\\)

Explanation:

Step1: Subtract the two equations

We have the system of equations:

$$\begin{cases} 6x - 3y = 12 \\ 4x - 3y = 24 \end{cases}$$

Subtract the second equation from the first equation:
$(6x - 3y)-(4x - 3y)=12 - 24$
Simplify the left - hand side: $6x-3y - 4x + 3y=2x$
Simplify the right - hand side: $12-24=-12$
So we get $2x=-12$

Step2: Solve for x

Divide both sides of the equation $2x = - 12$ by 2:
$x=\frac{-12}{2}=-6$

Step3: Substitute x into one of the original equations

Substitute $x = - 6$ into the first equation $6x-3y = 12$:
$6\times(-6)-3y = 12$
Calculate $6\times(-6)=-36$:
$-36-3y = 12$

Step4: Solve for y

Add 36 to both sides of the equation $-36 - 3y=12$:
$-3y=12 + 36$
$12 + 36 = 48$, so $-3y=48$
Divide both sides by - 3:
$y=\frac{48}{-3}=-16$

Answer:

The solution to the system of equations is $x=-6,y = - 16$