Question

1. 3x + 10y = 30

-4x - 10y = -20

Explanation:

Step1: Add the two equations

We have the system of equations:

$$\begin{cases}3x + 10y = 30\\-4x - 10y = -20\end{cases}$$

Adding the left - hand sides and the right - hand sides of the two equations respectively:
$(3x + 10y)+(-4x - 10y)=30+(-20)$
Simplify the left - hand side: $3x + 10y-4x - 10y=-x$
Simplify the right - hand side: $30 - 20 = 10$
So we get the equation: $-x=10$

Step2: Solve for x

Multiply both sides of the equation $-x = 10$ by - 1, we have $x=-10$

Step3: Substitute x into one of the original equations to solve for y

Substitute $x = - 10$ into the first equation $3x+10y = 30$:
$3\times(-10)+10y=30$
Simplify the left - hand side: $-30 + 10y=30$
Add 30 to both sides of the equation: $10y=30 + 30=60$
Divide both sides of the equation by 10: $y = 6$

Answer:

The solution of the system of equations is $x=-10,y = 6$