Solving equations graphically.

Before I start, if this is the wrong section, I'm sorry, I don't really know which section to post it on.

How do I solve these equations graphically :

x+2y=7

x+y=3

This is how I work it out, but for some reason I'm not getting the correct answer, even though I've used it to solve other equations like this :

x+2y=7

Let x=0

0+2y=7

2y=7

y=3.5

Co-ordinate points=(0,3.5)

x+2y=7

Let y=0

x+2(0)=7

x=7

Co-ordinate points=(7,0)

x+y=3

Let x=0

0+y=3

y=3

Co-ordinate points=(0,3)

x+y=3

Let y=0

x+0=3

x=3

Co-ordinate points=(3,0)

So, as we can see, the points for the first equation the co-ordinate points I plot are (0,3.5) and (7,0) and for the second equation I plot (0,3) and (3,0).

The problem I'm having is when I plot them on the graph, they don't intersect, which means I don't have an answer. If they don't intersect, it must be wrong, but how, I think I've done everything correctly? Also, I've looked at other examples in my maths textbook and they work, but for some reason this one doesn't.

Please, please help. I have a test tomorrow and I really need to know how to do this.

Re: Solving equations graphically.

They do intersect, just not in the first quadrant.

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Re: Solving equations graphically.

Quote:

How do I solve these equations graphically :

x+2y=7

x+y=3

$\displaystyle x+2y = 7$

change to slope-intercept form ...

$\displaystyle 2y = -x + 7$

$\displaystyle y = -\frac{x}{2} + \frac{7}{2}$

$\displaystyle x+y = 3$

change to slope-intercept form ...

$\displaystyle y = -x+3$

graph them ...