Question

Can someone help me solve this equations graphically? 3y+2x=4 4y+5x=3

Answer 1

the first step is graph the two equations
3y+2x=4
I would look for 2 points on this line.
pick a y, for example y=0. now find x. can you do that?

Answer 2

Find x for both of the equations?

Answer 3

no. one equation at a time. first let's work on
3y+2x=4

Answer 4

Ok so 3(0)+2x=4 so x+2, right?

Answer 5

you mean x=2. so one point on this line (it's a line by the way) is (2,0)
now try y=2 (I think we get a nicer number than if we used y=1)

Answer 6

Yes! Sorry. so x=-4!

Answer 7

(2,-4)

Answer 8

(-4,2)

Answer 9

I got something different. how did you get -4?

Answer 10

3y+2x=4 with y=2
3*2+2x=4
6+2x=4
2x= 4-6
2x=-2
x=-1

Answer 11

Oh, my bad. Thanks though, So how many points do you think i should make for the graph?

Answer 12

you only need 2 points.

Answer 13

Ah, true. Thanks! I really appreciated your help. :)

Answer 14

so the 2 points you have for the first equation are
(2,0) and (-1,2)

Answer 15

you plot those points and draw a line through them.

now we need 2 points on the other line
4y+5x=3

another way to plot this is put it in slope intercept form
y= mx+b

solve for y: 4y= -5x+3
y= -5/4 x +3/4
its y-intercept is 3/4 so one point is (0, 3/4)

Answer 16

using
y= -5/4 x +3/4
with x=1 we get y= -5/4 +3/4 = -2/4 = -1/2
so (1, -1/2) is another point

two points for the 2nd line:
(0, 3/4)
(1, -1/2)

Answer 17

can you plot those points?

Answer 18

if you can, then plot the points, draw a line through them.
Look for where the 2 lines cross. that is the "solution"
I would read the (x,y) point where the lines meet, and test that they work in both equations (as a check)