Question

PLEASE HELP!!!!! 90 POINTS!!!!!

Graph the following system of equations.

2x + 4y = 8
2x + 6y = 18

What is the solution to the system?

There is no solution.
There is one unique solution, (−6, 5).
There is one unique solution, (−4, 4).
There are infinitely many solutions.

Answer 1

Answer is in the graph, there is one unique solution (-6, 5)

The question asks you to graph and find the solution. I graphed this and attached it.

The solution is where the lines intersect, at (-6, 5)

Answer 2

There is one unique solution, (−6, 5).

Explanation:

2x + 4y = 8

2x + 6y = 18

2x + 4y = 8 ==> solve for 2x

2x + 4y - 4y = 8 - 4y

2x = 8 - 4y

2x + 6y = 18 ==> solve for 2x

2x + 6y - 6y = 18 - 6y

2x = 18 - 6y

8 - 4y = 18 - 6y ==> 2x = 8 - 4y and 2x = 18 - 6y

8 - 4y + 6y = 18 - 6y + 6y ==> solve for y by first adding 6y on both sides to

remove negative y

8 + 2y = 18 ==> simplify

8 - 8 + 2y = 18 - 8 ==> isolate y

2y = 10

y = 5

2x + 4(5) = 8 ==> substitute 5 for y in 2x + 4y = 8

2x + 20 = 8

2x - 20 + 20 = 8 - 20 ==> subtract 20 on both sides to isolate 2x

2x = -12

x = -6

x = -6, y = 5 ==> (6, 5)

Answer: There is one unique solution, (−6, 5).