Question

2. Solve the system by substitution.
2x - y + z = -4
z= 5
-2x +3y - z = -10


(1 point)
(–8, 7, 5)
(–8, –7, 5)
(8, –7, 5)
(–8, –7, –5)

Answer 1

To begin, try substituting z=5 into the first equation and solve for y.

Answer 2

Substituting z=5 into the first equation, you get:
2x-y+z=-4
2x-y+(5)=-4
2x-y=-9
2x+9=y
So, y=2x+9.

Now, substitute y=2x+9 into the third equation.

Answer 3

Substituting z+5 and y=2x+9 into the third equation, you get:
-2x+3y-z=-10
-2x+3(2x+9)-(5)=-10
-2x+6x+27-5=-10
4x+22=-10
4x=-32
x=-8

So, you now know that x=-8 and z=5. Substitute x=-8 into y=2x+9 to find y.

Answer 4

okay. Thank you so much. I was having trouble understanding this problem but now I get it.

Answer 5

You're very welcome.

Answer 6

does Y= 25 or did i solve it wrong?

Answer 7

Remember that x=-8, so when you substitute it into y=2x+9 you get:
y=2x+9
y=2(-8)+9
y=-16+9
y=-7

Answer 8

oh okay. thanks again.

Answer 9

Yeah. No problem.