Question

1. \

$$\begin{cases} 6x + 5y = 4 \\\\ 6x - 7y = -20 \\end{cases}$$

Explanation:

Step1: Subtract the two equations

We have the system of equations:

$$\begin{cases}6x + 5y = 4 \\ 6x - 7y = -20\end{cases}$$

Subtract the second equation from the first equation:
$$(6x + 5y)-(6x - 7y)=4-(-20)$$
Simplify the left - hand side: $6x + 5y-6x + 7y = 12y$
Simplify the right - hand side: $4 + 20=24$
So we get the equation $12y = 24$

Step2: Solve for y

Divide both sides of the equation $12y = 24$ by 12:
$y=\frac{24}{12}=2$

Step3: Substitute y into one of the original equations

Substitute $y = 2$ into the first equation $6x+5y = 4$:
$6x+5\times2 = 4$
$6x+10 = 4$
Subtract 10 from both sides: $6x=4 - 10=-6$
Divide both sides by 6: $x=\frac{-6}{6}=-1$

Answer:

The solution of the system of equations is $x=-1,y = 2$