# Thread: System of Equations?

1. ## System of Equations?

Consider the following system of three equations in three unknowns.
2x − y + z = −9
x + y + 4z = −17
3x + 4y − z = 2

(a) Solve the first equation for z.

z = -9-2x+y

(b) Put the solution you got in part (a) for z into both the second and third equations. Solve each equation for y.

2nd equation y = (19+7x)/5
3rd equation y = (-7-5x)/3

(c) Solve the system of two equations in two unknowns that you found in part (b).

(x,y) =

(d) Write the solution of the original system of three equations in three unknowns.

(x,y,z) =

I'm not quite sure how to get the points. Do I use the second or first equation, substitute y and z and solve for x? I don't even know how to begin to solve for z...

2. Originally Posted by MathBane
Consider the following system of three equations in three unknowns.
2x − y + z = −9
x + y + 4z = −17
3x + 4y − z = 2

(a) Solve the first equation for z.

z = -9-2x+y

(b) Put the solution you got in part (a) for z into both the second and third equations. Solve each equation for y.

2nd equation y = (19+7x)/5
3rd equation y = (-7-5x)/3

(c) Solve the system of two equations in two unknowns that you found in part (b).

(x,y) =

(d) Write the solution of the original system of three equations in three unknowns.

(x,y,z) =

I'm not quite sure how to get the points. Do I use the second or first equation, substitute y and z and solve for x? I don't even know how to begin to solve for z...
Set the 2nd and 3rd equation equal to eachother, this will get you x and y, then plug these points into z=-9-2x+y to get z