Question

3x + 2y = 9 and 2x + 6y = 6

Answer 1

3x + 2y = 9 (1)

2x + 6y = 6 (2)

We need to eliminate one of them

So let us at first divide equation (2) by 2 to simplify it

`\begin{gathered} (2x)/(2)+(6y)/(2)=(6)/(2) \\ x+3y=3 \end{gathered}`

x + 3y = 3 (3)

Now we can multiply equation (3) by -3 to eliminate x

-3(x) + -3(3y)=-3(3)

-3x - 9y = -9 (4)

Now add equations (1) and (4)

(3x - 3x) + (2y - 9y) = (9 -9)

0 - 7y = 0

-7y = 0

Divide both sides by -7

`(-7y)/(-7)=(0)/(-7)`

y = 0

Now substitute the value of y in equation (1) or 2 to find x

I will take (1)

3x + 2(0) = 9

3x + 0 = 9

3x = 9

Divide both sides by 3 to find x

`(3x)/(3)=(9)/(3)`

x = 3

The solution of this system of equations is (3, 0)