Question

Could someone PLEASE help me?!
Match each system of linear equations with the quadrant in which the solution lies.

Match Term Definition
3x – 2y = 10
5x + 3y = 4 A) III
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3x + 2y = 14
x – 3y = –10 B) I
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x + 2y = 8
4x + 6y =22 C) II
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2x + 3y = –12
4x – 2y = –2 D) IV

Answer 1

I would assume the following procedure would apply to the remaining three:
For the linear equations
\[3x-2y=10\] and \[5x+3y=4\]
Put the two equations in terms of y=, so
\[3x-2y=10 \rightarrow 2y=3x-10 \rightarrow y= \frac{3x-10}{2}\]
\[5x+3y=4 \rightarrow 3y=4-5x \rightarrow y=\frac{4-5x}{3}\]
Because both are of the form "y=", we can set the two equations equal to one another:
\[y= \frac{3x-10}{2} = \frac{4-5x}{3}\]
Solve for x by performing cross multiplication:
\[3*(3x-10) = 2*(4-5x)\]
\[9x-30 = 8-10x\]
\[19x = 38 \rightarrow x=\frac{38}{19}\]
Now plug that value of x into your original equation and find the y-value corresponding to that x that we just found. After that, you should have a coordinate (x,y), and looking at that, you should know which quadrant the two lines intersect.