1. ## linear equations

this is the question

John bought 3 shirts and 4 pairs of socks for $78. Joan bought 2 shirts and 6 pairs of socks for$72.

Letting $x equal the price of a shirt and$y equal the price of a pair of socks, write a linear equation to represent each transaction.
Draw on the same axes the graphs of the two equations. Read off the co-ordinates of the point of intersection to find the values of x and y.

i came up with this
3x + 4y = 78

2x+ 6y = 72

howeve, im not sure how do the graphany help on this ould be cool

2. 3x + 4y = 78
2x+ 6y = 72

Lets arrange these two equations such that they are in y=mx+b form.

3x + 4y = 78
4y = 78 - 3x
4y = 3(26-x)
y = (3/4) (26-x)

2x+6y = 72
6y = 72-2x
6y = 2 (36-x)
y = (1/3) (36-x)

Now can you graph these? If you must, you can always google "online graphing calculator" or something like that.

To find the point of intersection, let's just set the two equations (in y=mx+b form) equal to one another. So, we have: (3/4) (26-x) = (1/3) (36-x). Find x and then plug in your value for x into either of the equations to determine your y-value. Then you will have your point of intersection in the form (x,y).

-Andy

3. Originally Posted by realistic
this is the question

John bought 3 shirts and 4 pairs of socks for $78. Joan bought 2 shirts and 6 pairs of socks for$72.

Letting $x equal the price of a shirt and$y equal the price of a pair of socks, write a linear equation to represent each transaction.
Draw on the same axes the graphs of the two equations. Read off the co-ordinates of the point of intersection to find the values of x and y.

i came up with this
3x + 4y = 78

2x+ 6y = 72

howeve, im not sure how do the graphany help on this ould be cool

Originally Posted by abender
3x + 4y = 78
2x+ 6y = 72

Lets arrange these two equations such that they are in y=mx+b form.

3x + 4y = 78
4y = 78 - 3x
4y = 3(26-x)
y = (3/4) (26-x)

2x+6y = 72
6y = 72-2x
6y = 2 (36-x)
y = (1/3) (36-x)

Now can you graph these? If you must, you can always google "online graphing calculator" or something like that.

To find the point of intersection, let's just set the two equations (in y=mx+b form) equal to one another. So, we have: (3/4) (26-x) = (1/3) (36-x). Find x and then plug in your value for x into either of the equations to determine your y-value. Then you will have your point of intersection in the form (x,y).

-Andy
Great work abender! Here's a graph to verify what you have done:

--Chris

4. Originally Posted by Chris L T521
Great work abender! Here's a graph to verify what you have done:

--Chris
i can see now for:

3x + 4y =78
y = -(3/4)x + 19.5

2x + 6y = 72
y = -(1/3)x +12

{x, -0, 20} this part

5. Originally Posted by realistic
i can see now for:

3x + 4y =78
y = -(3/4)x + 19.5

2x + 6y = 72
y -(1/3)x +12

{x, -0, 20} this part
Oh. That last bit is code that is required for mathematica to plot the graph. I input some domain, and it graphs the set of functions within that specified domain. It has nothing to do with the problem.

The stuff above the graph is the code that outputs the graph.

I hope that this didn't cause much confusion...

--Chris

6. Originally Posted by Chris L T521
Oh. That last bit is code that is required for mathematica to plot the graph. I input some domain, and it graphs the set of functions within that specified domain. It has nothing to do with the problem.

The stuff above the graph is the code that outputs the graph.

I hope that this didn't cause much confusion...

--Chris
In the question it also asks me to write a linear equation to represent each transaction. (which I understand thanks to you guys)

But also I have to:

Draw on the same axes the graphs of the two equations. Read off the co-ordinates of the point of intersection to find the values of x and y.

this part im struggling with

7. Originally Posted by realistic
In the question it also asks me to write a linear equation to represent each transaction. (which I understand thanks to you guys)

But also I have to:

Draw on the same axes the graphs of the two equations. Read off the co-ordinates of the point of intersection to find the values of x and y.

this part im struggling with
What you would need to do is this:

You know what the y intercepts are from the equations.

What we need to find now is where they cross the x axis. Then drawing the line is a piece of cake.

To do this, set y in both equations equal to 0:

This tells us where they will cross the x axis. The graph verifies this:

Again, don't get confused, the top part of the graph is the code that generates the graph...

To find the intersection point, set the two equations equal to each other:

The graph verifies what we have done:

Does this make more sense now?

--Chris