Question

2. Solve each equation using addition, (2x + 2y = -2 3x – 2y = 12

Answer 1

The given pair of equation :

2x + 2y =-2

3x-2y=12

We can solve the the equation by using substitution method

Simplify the first equation and solve for y and then put this value of y in second equation to solve for x

2x+2y=-2

Divide equation by 2

x+y=-1

y = -1-x

Substitute the value of y=-1-x in the second equation

`\begin{gathered} 3x-2y=12 \\ 3x-2(-1-x)=12 \\ 3x+2+2x=12 \\ 5x=12-2 \\ 5x=10 \\ x=2 \\ \text{ Use this value of }x=2\text{ in the first equation and solve for y} \\ 2x+2y=-2 \\ 2(2)+2y=-2 \\ 4+2y=-2 \\ 2y=-2-4 \\ 2y=-6 \\ y=(-6)/(2) \\ y=(-3) \end{gathered}`

So, the value of x =2 & y = (-3)

Answer : (x, y) = (2, -3)