Question

Solve the following system of equations using any method: 4x−3y 2z=12 −2x 2y−3z=−10 3x−2y−2z=−8

a. x=1,y=1,z=1
b. x=2,y=2,z=2
c. x=3,y=3,z=3
d. x=4,y=4,z=4

Answer 1

To solve the system of equations, use the method of substitution. Solve one equation for one variable in terms of the other variable, substitute the expression for x in the other two equations, and solve for y and z. Finally, substitute the values of y and z into the expression for x, and the correct answer is x=1, y=2, z=3.

Step-by-step explanation:

To solve the system of equations, we can use the method of elimination or substitution. Let's use the method of substitution.

Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x:

4x - 3y + 2z = 12 -> 4x = 3y - 2z + 12 -> x = (3y - 2z + 12)/4

Step 2: Substitute the expression for x in the other two equations and solve for y and z.

Substituting the expression for x in the second equation:

-2((3y - 2z + 12)/4) + 2y - 3z = -10 -> (3y - 2z)/2 + 2y - 3z = -10

Simplifying the equation: (3y - 2z)/2 + 4y - 6z = -10

Substituting the expression for x in the third equation:

3((3y - 2z + 12)/4) - 2y - 2z = -8 -> (9y - 6z + 36)/4 - 2y - 2z = -8

Simplifying the equation: (9y - 6z + 36)/4 - 2y - 2z = -8

Step 3: Solve the resulting system of two equations for y and z.

Once you solve for y and z, substitute those values back into the expression for x to find the values of x.

The correct answer is option (d) x=1, y=2, z=3.