Consider the following system of equations:

Question

2x + 3y = 12
—4x + 5y = —4
Which of the following equations could be used to create
an equivalent system (a system with the same solution) ?
Select all the apply.

Answer 1

-4(2x + 3y) = -4(12)
8x + 12y = -48

2(4x + 5y) = 2(-4)
8x + 10y = -8

Both of these equations can be used to create an equivalent system.

Answer 2

Consider the following system of equations:
3x-5y=4
5x + y = 16
Determine the y —coordinate of the solution of the
system.

Answer 3

To determine the y-coordinate of the solution, we can solve this system of equations by elimination or substitution method.

Given equations:
3x - 5y = 4 ...(1)
5x + y = 16 ...(2)

First, we can solve equation (2) for y:
y = 16 - 5x

Now substitute this value of y in equation (1):
3x - 5(16 - 5x) = 4
3x - 80 + 25x = 4
28x - 80 = 4
28x = 84
x = 3

Now, substitute x = 3 back into equation (2):
5(3) + y = 16
15 + y = 16
y = 1

The y-coordinate of the solution to the system of equations is y = 1.