Question

GIVING 75 POINTS please answer the question attached<3 as soon as possible thank you!

how many solutions does the system of equations have? 6x+18y=9 and y=-1/3x+1/2

Answer 1

Answer:

D) Infinitely many

Step-by-step explanation:

Given system of equations

$\left \{ {{6x+18y=9} \atop {y=-\frac{1}{3}x+\frac{1}{2} }} \right.$

Substitute second equation into first equation

$6x+18y=9\\\\6x+18(-\frac{1}{3}x+\frac{1}{2})=9\\ \\6x-6x+9=9\\\\9=9$

Therefore, since both sides are equal to each other no matter what, there are infinitely many solutions.

You can confirm that there are infinitely many solutions by looking at the graph of both functions. They overlap each other, so every solution will work.

Answer 2

Answer:

• Infinitely many solutions

Step-by-step explanation:

Given:

• 6x + 18y = 9
• y = -1/3x + 1/2

Solution:

• 18y = -6x + 9

         y = -1/3x + 1/2  

• => 18y = -6x + 9

            18(y = -1/3x + 1/2)

• => 18y = -6x + 9

            18y = -6x + 9

Since both the equations are the same, this system of equations has infinitely many solutions.