Question

What is the solution to the system?

2x+3y=11
3x+3y=18

Answer 1

Have you attempted solving it?

Answer 2

Choices:
(7, -3)
(7, 25/3)
(7, -1)
(-7, 25/3)

Answer 3

Yeah, if I knew how to do it I wouldn't be asking.

Answer 4

Okay, first, to get the x coordinate, take away the y variabl altogether

Answer 5

Ok, there are several methods for solving a system of equations.
For this system of equations, elimination seems to be the easiest method.

Using the elimination method, we add or subtract equations with the goal of eliminating a variable.

Notice that both equations have 3y.

Answer 6

I did that part. I ended up getting \[x=\frac{ 11 }{ 2 }-\frac{ 3y }{ 2 }\]

Answer 7

Subtract the first equation from the second equation.

Answer 8

I started doing substitution, I'm not so good with elimination. But I'd like to know how to do it.

Answer 9

Let's finish the problem using substitution since you started that already, and you did that correctly.

Answer 10

Then we can also do elimination afterwards.

Answer 11

You solved the first euqtion for x.
You did it correctly.
Now insert what x is equal to in x of the second equation.

Answer 12

I got (7,-1)

Answer 13

First equation solved for x:

\(x=\color{red}{\dfrac{ 11 }{ 2 }-\dfrac{ 3y }{ 2 }}\)

Second equation:

\(3x+3y=18\)
Divide both sides by 3:
\(\color{red}{x} + y = 6\)

Replace x by what x is equal to:

\( \color{red}{\dfrac{11}{2} - \dfrac{3y}{2}} + y = 6\)

Multiply both sides by 2:

\(11 - 3y + 2y= 12\)

\(-y = 1\)

\(y = -1\)

Now substitute y = -1 into the first original equation:

2x + 3(-1) = 11
2x - 3 = 11
2x = 14
x = 7

Solution: (7, -1)

You are correct.

Answer 14

Thank you!!! :)

Answer 15

wlcm