Question

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 5x+7=2y and y-9x=23

A) {}
B) 1 solution
C) Infinite

Answer 1

Answer: Option B

The system has 1 solution

Explanation:

We must solve the following system of equations

`5x+7=2y\\\\y-9x=23`

To solve it, clear y from the second equation and then substitute in the first equation

`y=23 + 9x`

Now substitute in the first equation

`5x+7=2(23 + 9x)\\\\5x +7 = 46 + 18x\\\\5x -18x = 46-7\\\\-13x = 39\\\\x = -(39)/(13)\\\\x=-3`

Answer 2

The correct option is option B. It has one solution, and it's x=-3

Explanation:

We have the following system of equations:

5x+7 = 2y (1)

y-9x=23 (2)

Step 1: Solve for 'y' in equation (2):

y-9x = 23

y = 9x + 23

Step 2: Substitute in equation (1):

5x + 7 = 2y

5x + 7 = 2(9x + 23)

5x + 7 = 18x + 46

Step 3: Solve for x:

7 - 46 = 18x - 5x

-39 = 13x

x= -3

So the correct option is option B. It has one solution, and it's x=-3