Question

Use the substitution method to solve the following system of equations.

4x – y – 3z = –3
x – 2y – 2z = –3
x + y + 3z = –2

Answer 1

Hint: Solve the second equation for x to get

x – 2y – 2z = –3

x = 2y+2z–3

Then plug this into the first equation to get

4x – y – 3z = –3

4(2y+2z–3) – y – 3z = –3

8y + 8z - 12 - y - 3z = -3

7y + 5z - 12 = -3

7y + 5z = -3+12

7y + 5z = 9

Then plug x = 2y+2z–3 into the third equation

x + y + 3z = –2

2y+2z–3 + y + 3z = –2

3y + 5z - 3 = -2

3y + 5z = -2+3

3y + 5z = 1

Answer 2

So you should end up with this new system of equations

7y + 5z = 9
3y + 5z = 1

Solve this system (ignore the other equations or previous system) for y and z.

Once you have y and z, use them to find x.