For answering multiple choice, you can do the following:
Observe the diagram, noting that one curve has positive slope, and the other has negative slope. Looking at the equations, if x and y are on the same side of the equal sign, (which is the case here), then - coefficients of x and y have equal signs (both+, or both -) then the equation has negative slope. - coefficients of x and y have different signs (+-, or -+), then the equation has positive slope. We see the second system has both equations with positive slope, and the third system has both equations with negative slopes. They're out!
Next, we check the y-intercept of the first equation (by setting x=0), first system: 0+2y=-10 => y-intercept=-5, slope=-1/2 Good fourth system: 0-2y=-10 => y-intercept=+5 No good.
Finally, check the x-intercept of the second equation of the first system (by setting y=0) first system: 3x-0=12 => x-intercept = 12/3=+4, slope = +3 good
So we conclude the first system is the correct answer.
