1. What is the solution to the system of equations?
{−2x + 6y = −38
3x − 4y =
A.(4, −5)
B.(−5, 4)
C.(1, −6)
D. (−4, −5)
2.What is the solution to the system of equations?
x + 3y − z = 6
4x − 2y + 2z = −10
6x + z = −12
A. (−4, 0, 12)
B. (−3, 5, 6)
C. (2, 1, −3)
D. (0, −2, −12)
2.
___ | ___ | ____ | ________________________________ | ___ | ___ | ____ | ||||||||
x | + | 3y | - | z | = | 6 | multiply through by 2 to get | 2x | + | 6y | - | 2z | = | 12 |
4x | - | 2y | + | 2z | = | -10 | multiply through by 3 to get | 12x | - | 6y | + | 6z | = | -30 |
6x | + | z | = | -12 | multiply through by -4 to get | -24x | - | 4z | = | 48 |
Add these three equations together to get
-10x = 30 Divide both sides by -10 .
x = -3
Use this value for x in the third given equation to find z .
6(-3) + z = -12 Subtract 6(-3) from both sides.
z = -12 - 6(-3) = -12 + 18 = 6
Now we can find y using the first given equation.
-3 + 3y - 6 = 6
3y = 15
y = 5
So x = -3 , y = 5 , and z = 6