How do I use a graph to solve the system of equations #3x+4y=10# and #x−y=1#?

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Answer 1 · 2015-07-09T19:42:41

You graph the equations and see where they intersect.

Your equations are

#3x+4y = 10#
#x-y = 1#

Let's rearrange these to

(1) #y = 1/4(10-3x) = -3/4 x + 5/2#
(2) #y = x-1#

Plot the graph of Equation 1.

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Now add the graph for Equation 2.

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The two lines intersect at (#2,1#).

The solution is #x = 2#, #y = 1#.

Check:

#3x+4y = 3×2+4×1 = 6+4 = 10#

#x-y = 2-1 = 1#