Question

What is the solution to the system of equations shown below?

x-­ y + z = 0

­-5x + 3y ­- 2z = ­-1

2x ­ - y + 4z = 11


a. (0, 3, 3)

b. (2, 5, 3)

c. no solution

d. infinitely many solution

p.s i dont care about explaining your answer i can figure it out thanks :)

Answer 1

b., (2, 5, 3).

Explanation:

x-­ y + z = 0

-5x + 3y ­- 2z = ­-1

2x ­ - y + 4z = 11

Multiply the first equation by 2

2x - 2y + 2z = 0

Adding this to the second equation we get

-3x + y = -1 ........... (A)

Multiplying the second equation by 2 and adding to the third equation we get:

-8x + 5y = 9................(B)

Multiplying equation (A) by -5 and adding to equation (B) we get:

7x = 14

x = 2.

Substituting -3(2) + y = -1 so y = -1 + 6 = 5.

And substituting in the first equation fo x and y:

2 - 5 + z = 0

z = 5-2 = 3.

Answer 2

b. (2, 5, 3)

Explanation:

Trying the offered choices seems the fastest way to find the answer. The second choice works in all equations, hence is the solution.

Another strategy you can use is to see if the equations are dependent. Here, it looks like adding twice the third equation to the other two eliminates at least the x- and y-variables. If that eliminates z, then there are infinite solutions. Instead, it gives the equation ...

7z = 21

z = 3 . . . . . divide by 7

This answer is consistent with choice B, confirming that answer and eliminating the other choices.