Question

Solve this system by substitution (3 variables) with steps:

-x -y -z = -8
-4x +4y +5z = 7
2x+2z=4

Answer 1

To solve this system by substitution, rearrange one equation to solve for a variable and substitute it into the other equations. Simplify and solve the resulting system to find the values of the variables. Substitute the values back to find the solution.

Step-by-step explanation:

To solve this system by substitution, we need to isolate one variable in terms of the other variables in one of the equations and substitute it into the other equations.

Step 1: Rearrange the first equation to solve for x: x = -8 - y - z.

Step 2: Substitute the expression for x into the remaining two equations: -4(-8 - y - z) + 4y + 5z = 7 and 2(-8 - y - z) + 2z = 4.

Step 3: Simplify and solve the resulting system of equations to find the values of y and z.

Step 4: Substitute the values of y and z back into the expression for x to find the value of x.

The solution to the system of equations is x = -3, y = 2, and z = 0.