Question

Solve the system by substitution.
2x +y+z= 12
5x + 5y + 5z = 20
х- 4y +z= -21

Answer 1

(x, y, z) = (8, 5, -9)

Explanation:

Using the first equation, we can write an expression for z:

z = 12 -2x -y

We can substitute this into the other two equations. (Before we do that, we'll divide the second equation by 5.)

x + y + (12 -2x -y) = 4 ⇒ -x +12 = 4

x -4y +(12 -2x -y) = -21 ⇒ -x -5y +12 = -21

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The first of these gives us a value for x:

8 = x . . . . add x-4 to both sides

Using this in the second equation of these, we have ...

-8 -5y +12 = -21

-5y = -25

y = 5

Then the value of z is ...

z = 12 -2(8) -5

z = -9

The solution to the system is (x, y, z) = (8, 5, -9).