Question

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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

Answer 1

Answer:

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

Answer 2

Answer:

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.