Question

Solve the Equation
5x+15y=10
5x-10y=-40

Answer 1

x = -4, y = 2

Explanation:

`\left\{\begin{array}{ccc}5x+15y=10\\5x-10y=-40&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}5x+15y=10\\-5x+10y=40\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad25y=50\qquad\text{divide both sides by 25}\\.\qquad\qquad\boxed{y=2}\\\\\text{Put the value of y to the first equation:}\\\\5x+15(2)=10\\5x+30=10\qquad\text{subtract 30 from both sides}\\5x=-20\qquad\text{divide both sides by 5}\\\boxed{x=-4}`

Answer 2

Explanation:

-5x + 10 = 15y

(-5(x-2))/15

(-x+2)/3 = y

5x - 10((-x+2)/3)

5x - ((-10x + 20)/3)=-40

5x + (10x-20)/3

15x + 10x - 20 = -120

25x = -100

x = -4

5x + 15y = 10

-20 + 15y = 10

30 = 15y

y = 2