Question

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 1

-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.

Answer 2

`\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}`