Question

solve the following system of equations express your answer as an ordered pair in the format (a,b) with no spaces between the number or symbols 3x+4y=16 -4x-3y=-19 please help :)

Answer 1

Ok, so first we need to find where these lines intersect. We can use substitution, elimination, or we can graph it. Do you have a preference?

Answer 2

no not really anything will work

Answer 3

Ok. Let's solve it by substitution. That' seems like it will be the easiest. First let's rewrite the first equation (3x+4y=16) so we have y = something, then we'll substitue that in to the other equation.
3x+4y=16
4y=-3x+16
y=-3/4x+4

Now we can substitute this into the other equation. You still following me?

Answer 4

kinda

Answer 5

Ok. So now that we have y = -3/4x+4, we can put this in for y in the other equation to find what x is. That's what I mean by "substitute it in."
Our second equation was
-4x-3y=-19
Now we'll put in what y is
-4x-3(-3/4x+4)=-19
-4x+9/4x-12=-19
-4x+9/4x = -7
-7/4x = -7 ---Multiply both sides by 4
-7x = -28 ---Divide both sides by 7
-x = -4
x = 4

Now that we know what x is, we can put x (which is really 4) into one of the equations and then solve for y, this will tell us where the lines intercept, which is what we're trying to figure out.

Answer 6

okay how does the get us to our final answer as an ordered pair ?

Answer 7

Once we find what x and y is, that's where they intercept and we can write that as an ordered pair as (x,y)
Now we need to find what y is. So let's put x into the original first equation
3x+4y=16
3(4)+4y=16
12+4y=16 ---Subtract 12 from both sides
4y=4 ---Divide both sides by 4
y=1

Alright, so our ordered pair is (4,1)
Here's an attached graph to show you this if it helps you visualize it:

Answer 8

thanks i have a better understanding now :)

Answer 9

Glad to help. I probably could have explained it a little better but I'm glad you understand it. :)