Question

Solve the system of equations and choose the correct ordered pair 4x-2y=-2 6x+3y=27

Answer 1

Elimination method

We need one variable to cancel with the other if we were to add or subtract the equations from each other. I will eliminate y in the following way:

Multiply to get common coefficient
4x - 2y = -2 multiplied by 3:
12x - 6y = -6

6x + 3y = 27 multiplied by 2:
12x + 6y = 54

Im going to add these but in this case, adding them would also cancel out a different variable.
12x - 6y = -6
+
12x + 6y = 54
—————————-
24x = 48
24/24 x = 48/ 24

x = 2

Now we have to find Y by using the x value in one of the original equations.

6(2) + 3y = 27
3y = 27 - 12
3y = 15
y = 5

Double check

4(2) - 2(5) = -2
8 - 10 = -2
-2 = -2

It is correct

X = 2 and Y = -2

Answer 2

First get rid of one variable

(4x-2y=-2) x3

(6x+3y=27) x2

12x-6y=-6

+ 12x+6y=54

solve for x

24x=48

x=2

Plug in and solve for y

8-2y=-2

-2y=-10

y=5

The ordered pair is (2,5)