How do you solve the following linear system: 2x + 4y = 7 , 3x + y = 4 2x+4y=7,3x+y=4?

1 Answer
Ken C.
Mar 19, 2016

(9/10, 13/10)(910,1310)
Refer below for explanation.

Explanation:

First, arrange them like this so you can compare terms:
2x+4y=72x+4y=7
3x+y=43x+y=4

When we solve linear systems like this, we always look for ways to cancel one variable. We can see that if we multiply 3x+y=43x+y=4 by -4−4, we will get a -4y−4y term. And then, if we add the new equation (with -4y−4y in it) to the other equation, the 4y4y and -4y−4y will cancel. Watch:
-4(3x+y=4)->-12x-4y=-16−4(3x+y=4)→−12x−4y=−16

-12xcancel(-4y)=-16
+2xcancel(+4y)=7
-----
-10x=-9
x=9/10

We can now use this x value to solve for y, like so:
2x+4y=7
2(9/10)+4y=7
9/5+4y=7
4y=7-9/5
4y=26/5
y=13/10

Therefore our solution is (9/10, 13/10). We can confirm this result in several ways. One, we can substitute these values into the original equations:
2x+4y=7->2(9/10)+4(13/10)=7->7=7
3x+y=4->3(9/10)+(13/10)=4->4=4

We can also look at the graph of these two equations, and confirm that they intersect at the point (9/10, 13/10).
enter image source here
Note that 9/10=0.9 and 13/10=1.3.

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