Question

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

x+2y-z=2
3x+y-2z=-15
3x+4y-3z=-2

Im lost!

Answer 1

first equation : x = 2 -2y + z

plug it into the second :
3(2-2y+z) + y -2z = -15
6 - 6y + 3z +y -2z = -15
z -5y = -21
z = -21 + 5y

now x become : x= 2 -2y + (-21 + 5y)
x = 2-2y-21+5y
x = 3y - 19

now plug z,x into the third equation :

3(3y-19) +4y - 3(5y-21) = -2
9y -57 +4y -15y + 63 = -2
-2y = -8
y = 4

now plug y into x and z equations :

x = 3*4 - 19 = -7
z = -21 +5*4 = -1

(-7,4,-1)

Answer 2

I got to -5y+z=-21 and I didnt know where to go from there. Thank You!