Hi! Can someone check these two answers? Thanks!

Directions: Find the correct number of solutions for the following system of equations.

1.) 5x - 3y + 2z = 3
2x + 4y-z = 7
x - 11y + 4z = 3

2.) 2x + y- 3z = 4
4x + 2z = 10
-2x + 3y - 13z = -8

A.) One Solution
B.) Infinitely Many Solutions
C.) No Solution

My answers:

1.) C.

2.) A.

1 answer

#1 C
#2 B

4x + 2z = 10, so z = 5-2x
That gives

2x + y - 3(5-2x) = 4
-2x + 3y - 13(5-2x) = -8
or
8x + y = 19
24x + 3y = 57
so, y = 19-8x

That is, whatever x you choose, y and z can be found.
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