Question

Solve this system of equations

x+y+z=6
2x-y+3z=9
2x+z=5

Answer 1

To solve this system of equations, we can use the method of substitution or elimination. Here, we will use substitution:

From the equation 2x + z = 5, we can solve for z in terms of x:
z = 5 - 2x

Substitute this expression for z in the first equation:
x + y + (5 - 2x) = 6

Simplify:
y - x + 5 = 6
y - x = 1

Now, we can substitute this expression for y in the second equation:
2x - (y - x) + 3z = 9

Simplify:
3x + 3z = 9

Substitute z in terms of x again:
3x + 3(5 - 2x) = 9

Simplify and solve for x:
3x + 15 - 6x = 9
-3x = -6
x = 2

Substitute x = 2 back into y - x = 1 to solve for y:
y - 2 = 1
y = 3

Substitute x = 2 back into z = 5 - 2x to solve for z:
z = 5 - 2(2)
z = 5 - 4
z = 1

So the solution to the system of equations is x = 2, y = 3, and z = 1.