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The graph of the following system of equations is (4 points)

-2x + y = 3
4x + 2y = 2

a. overlapping lines
b. parallel lines
c. intersecting lines



Answer :

[tex]\left\{\begin{array}{ccc}-2x+y=3\\4x+2y=2&|divide\ both\ sides\ by\ 2\end{array}\right\\\left\{\begin{array}{ccc}-2x+y=3&|add\ (-2x)\ to\ both\ sides\\2x+y=1&|subtract\ 2x\ from\ both\ sides\end{array}\right\\\left\{\begin{array}{ccc}y=2x+3\\y=-2x+1\end{array}\right\Rightarrow\ the\ slope \left\{\begin{array}{ccc}m=2\\m=-2\end{array}\right\ |different\\\\Conclusion:\ \boxed{\boxed{C}\ intersecting\ lines}[/tex]
Panoyin
-2x + 1y = 3 ⇒ 4x - 2y = -6
 4x + 2y = 2 ⇒ 4x + 2y = 2
                               -4y = -8
                                -4     -4
                                  y = 2
                      4x + 2(2) = 2
                          4x + 4 = 2
                                 -4  -4
                                4x = -2
                                 4      4
                                 x = -1/2
                             (x, y) = (-1/2, 2)
The answer to the problem is C. intersecting lines.

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