Question

The equations 3 x minus 4 y = negative 2, 4 x minus y = 4, 3 x + 4 y = 2, and 4 x + y = negative 4 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, negative 4) and (2, 4). Blue line goes through (negative 2, 2) and (2, negative 1). The pink line goes through (negative 2, negative 1), and (2, 2). The purple line goes through (negative 2, 4) and (0, negative 4). Which is the approximate solution for the system of equations 3 x + 4 y = 2 and 4 x + y = negative 4? (–1.4, 1.5) (1.4, 1.5) (0.9, –0.2) (–0.9, –0.2)

Answer 1

(–1.4, 1.5)

Explanation:

Answer 2

(–1.4, 1.5)

Explanation:

The blue line and the purple line are the lines corresponding to the equations of interest. Their point of intersection is in the 2nd quadrant, so is nearest to ...

(–1.4, 1.5)

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It can be useful to understand that for equations in standard form:

ax +by = c

the x- and y-intercepts are ...

• x-intercept: c/a . . . . value of x for y = 0
• y-intercept: c/b . . . . value of y for x = 0

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For the equations of interest, the first has intercepts of ...

x=2/3, y=1/2 . . . . graphed line makes a 1st-quadrant triangle with the axes (blue line)

And the second has intercepts of ...

x=-1, y=-4 . . . . graphed line makes a 3rd-quadrant triangle with the axes (purple line)

Since the purple line has a steeper slope, the point of intersection of the lines will be in the 2nd quadrant. There is only one 2nd-quadrant answer choice: (-1.4, 1.5).