`2x-3y=-3`
`-12=-4x+y`
In what quadrant willl the lines represented by the equations above intersect?

Options

A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV

Answer

A

Explanation

Difficult: Medium
Category: Heart of Algebra/ System of Linear Equations
Strategic Advice: Whenever you're asked to identify the quadrant in which the graphs of two lines intersect (not the exact values of x and y), drawing a quick sketch of the system of equations is likely to be the most time-efficient method to answer the question.
Getting to the Answer: Start by writting each equations in slope-intercept form `(y=mx+b)`:
`2x-3y=-3 to -3y=-2x-3 to y=(2)/(3)x+1`
`-12 =-4x+y to y=4x-12`
Then plot each y-intercept and use the corresponding slope to rise(or fall) and run to the next point. You don't have to be exact -no need to waste time drawing tick marks or labelling the graph - a sketch is all you need. (You can also graph the lines in your calculate if you prefer). Your graph might look something like this:

The lines intersect in quadrant I , which is (A).