Morgan,
Let equation (1) be: 2a-3b-3c=-7
Let equation (2) be: -4a-6b+2c=18
Let equation (3) be: -2a-3b+2c=14
Next, we need to eliminate equations down to 2 variables. First, let's start with equations (1) and (3) since we can eliminate a just by adding.
2a - 3b - 3c=-7
-2a - 3b + 2c=14
-6b - c = 7 make this equation (4)
Next, let's use equations (1) and (2) to eliminate a: To do this, multiply both sides of equation (1) by 2 to get:
2(2a-3b-3c)=-7(2)
4a - 6b - 6c= -14 Next add equation (2) to get:
-4a - 6b + 2c= 18
-12b - 4c = 4 Make this equation (5)
Now use equations (4) and (5) to solve for b and c.
-6b - c = 7 equation (4). Multiply by -2 on both sides.
12b +2c = -14
-12b - 4c = 4
-2c = -10
Therefore, c = 5.
Use equation (4) to solve for b:
-6b - c = 7
-6b -5 = 7
-6b = 12
Therefore, b = -2.
Now use equation (1) to solve for a:
2a-3b-3c=-7
2a -3(-2) -3(5) = -7
2a+6-15 =-7
2a -9 = -7
2a=2
Therefore, a = 1.
Check answers:
Equation (1) : 2a-3b-3c=-7 2(1) -3(-2) -3(5) = -7 -7 = -7 Checks!
Equation (2) : -4a-6b+2c=18 -4(1) -6(-2) +2(5) = 18 18 = 18 Checks!
Equation (3) : -2a-3b+2c=14 -2(1) -3(-2) +2(5) = 14 14 = 14 Checks!
Answers are a=1, b=-2, c=5.
Hope this helps!
