Question

Which point satisfies the system of equations y = 3x − 2 and y = -2x + 3?

Answer 1

Meet of lines: y = 3x − 2  and  y = -2x + 3?

y=3x-2 has slope 3 and y intercept -2 (which means thru (0,-2)) , so that's the blue line through point D.

y=-3x+3 has slope -2 and y intercept 3, so the red line through points A, C and  D.

The point D(1,1) is the intersection of the lines.  Let's check that algebraically:

3x-2=3(1)-2=1=y, good

-2x+3 = -2(1)+3=1=y, good

Answer: D