Question

50 points!
But DO NOT waste my points.
I will report you.

A student is trying to solve the system of two equations given below:

Equation P: y + z = 6
Equation Q: 3y + 4z = 1

Which of the following is a possible step used in eliminating the y-term?

a. (y + z = 6) ⋅ 4
b. (3y + 4z = 1) ⋅ 4
c. (y + z = 6) ⋅ −3
d. (3y + 4z = 1) ⋅ 3

c. (y + z = 6) ⋅ -3
Explanation:
Equation P : y + z = 6
Equation Q : 3y + 4z = 1
In order to solve by elimination and remove the y-term, the coefficients of y must be same or negative to each other in both the equations.
So to make the y co-efficient similar here, multiply the first equation by -3
When done: (y + z = 6) · -3 = -3y – z = -18
Solving steps:
-3y – 3z = -18
3y + 4z = 1
——————
z = -17
There the y-term has been removed.

c. (y + z = 6) ⋅ −3
Step-by-step explanation:
We want to use elimination to eliminate y in a system of equations
y + z = 6
3y + 4z = 1
We can take the first equation and multiply by -3 to make the y term -3 so when we add  the equations -3y + 3y =0
-3(y + z = 6)
3y + 4z = 1
——————–
-3y  -3z = -18
3y + 4z = 1
———————
0y  +z   = -17