Answer:
x = -2, y = 3, z = -6
Step-by-step explanation:
First, solve the third equation by substitution for variable z.
x - 5y + z = -23 -> z = -x + 5y - 23
In the first equation, plug the variable z in.
-x + 2y + 2z = -4
-x + 2y + 2 * (-x + 5y - 23) = -4
-x + 2y - 2x + 10y - 46 = -4
-3x + 12y = -4 + 46
-3x + 12y = 42
Do the same for the second equation.
4x + y - 3z = 13
4x + y - 3 * (-x + 5y - 23) = 13
4x + y + 3x - 15y + 69 = 13
7x - 14y = -56
Solve 7x - 14y = -56 for x.
Divide by 7 on both sides: x - 2y = -8
Express in terms of x: x = 2y - 8
Plug in x = 2y - 8 in the equation -3x + 12y = 42 to find y.
-3 * (2y - 8) + 12y = 42
-6y + 24 + 12y = 42
6y = 42 - 24
y = 3
Substitute your value of y into x = 2y - 8.
x = 2y - 8
x = 6 - 8
x = -2
We already substituted for variable z earlier, let's plug the values of x and y into the expression z = -x + 5y - 23 to find z.
z = -x + 5y - 23
z = 2 + 15 - 23
z = -6
