Linear equation word problems using substitution method

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SargeUSMC

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Sep 9, 2014
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I can't get off the ground with these problems:

9 guitars sold for $3611. Electric = $479. Acoustic = $339. How many of each?
x = electric
y = acoustic

x + y = 9?
479x + 339y = 3611?

I tried to solve this and it didn't fly.

76 tennis players playing 26 games. Doubles = 4 players. Singles - 2 players. How many of each match?
x = singles
y = doubles

x + y = 26?
2x + 4y = 76?

This doesn't work either.....
 
SargeUSMC said:
I can't get off the ground with these problems:

9 guitars sold for $3611. Electric = $479. Acoustic = $339. How many of each?
x = electric
y = acoustic

x + y = 9?
479x + 339y = 3611?

I tried to solve this and it didn't fly....
Click to expand...

Just the first one (and yes those are the correct equations):
x + y = 9?
479x + 339y = 3611?

So y = 9 - x and thus
479x + 339(9 - x) = 3611
140 x + 3051 = 3611
140 x = 560
x = 4
etc.

The equations are correct for the second one also.
 
figures..I had the right equations, but couldn't do the simple math!

thx a lot
 
I have a problem here where they want the answer in graphic form. What are they looking for.....an x, y point plotted on a graph?
 
Do you mean you have two equations and want a graphical solution to the system of equations? The whole point of graphing is that (x, y) is a point on the graph of an equation if and only if x and y satisfy the equation. So if an x, y pair satisfies both equations then it must lie on both graphs- it must be a point where the two graphs intersect. So draw the graph of each equation and determine where the intersect.

If these are still linear equations, that is particularly simple. The graph of a linear equation is a straight line and is determined by two points. Determine two x, y pairs for each equation, mark those two points on your graph and draw the line through them.
 
Ok, I understand the principle....plot both equations on a single graph, and the intersecting points are the solutions.

The 2 linear equations they want graphed (from the problem above) are:

x + y = 9 => y=9-x
479x+339y=3611 => y=3611-479x/339

The first one is simple enough to graph, but that 2nd one.....?? And given the numbers lowest to highest, how do I get them both on 1 graph?
 
SargeUSMC said:
Ok, I understand the principle....plot both equations on a single graph, and the intersecting points are the solutions.

The 2 linear equations they want graphed (from the problem above) are:

x + y = 9 => y=9-x
479x+339y=3611 => y=3611-479x/339

The first one is simple enough to graph, but that 2nd one.....?? And given the numbers lowest to highest, how do I get them both on 1 graph?
Click to expand...

First of all, be *very* careful about using grouping symbols (parentheses) when necessary. Failure to do so will result in math errors. Your second equation should be:

y= (3611-479x)/339

Next, don't worry about the big numbers in the equation. You already know that x and y have to be 0 through 9, right? So your graph only has to show that region for x and y. Plug in x = 0 and x = 9 into both equations and calculate the y values. Just plot those points.
 
yes....of course you are right. I see that now. Thank you for your help....

Francesca!! Where are you?? Dad is ready to help you with your homework!! hehehehe
 
I should amend my graphing a comments. Calculate the values of the points first, and use the answers as a guide to choosing your graph boundaries.
 
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