Question

1) Carefully follow the steps to find the solution to the three equation system.

1.)2x-4y+3z=-7
2.)x+2y+z=15
3.)-3x+y+z=2
a. Use equations 2 and 3 and eliminate the z by multiplication and addition, creating a new
equation with only z and y.
b. Use equations 1 and 3 and eliminate the z by multiplication and addition, creating a second
equation with only and y.
c. Use the two new equations, and eliminate the y-variable by multiplication and addition,
finding the value for the x-variable.
d. Substitute x-value in the first new equation and find the y-value.
e. Substitute the x- and y-values into original equation 2 to find the z-value.

answer option in picture

Answer 1

2,5,3

Explanation:

x=2

y=5

z=3

Answer 2

Explanation:

a. we simply subtract 3. from 2.

x + 2y + z = 15

- -3x + y + z = 2

--------------------------

4x + y 0 = 13

b. we multiply 3. by 3 and then subtract from 1.

2x - 4y + 3z = -7

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

-----------------------------

11x - 7y 0 = -13

c. we multiply the result of a. by 7, and then simply add a. and b., because the y terms have different signs already.

28x + 7y = 91

+ 11x - 7y = -13

--------------------------

39x 0 = 78

39x = 78

x = 2

d. we use this x = 2 in the result of a.

4×2 + y = 13

8 + y = 13

y = 5

e. using x = 2 and y = 5 in 2.

2 + 2×5 + z = 15

2 + 10 + z = 15

12 + z = 15

z = 3

the solution is therefore (2, 5, 3).