You guys : ) which ordered pair (x, y) is a solution to the following system of equations? {5x+4y=-14} {3x+6y=6} answer choices: a. (-6,4) b. (2/7,18/7) c. (18/7,2/7) d. (6,-2)

There is a long way - but I like the short way!

There is only one correct solution so why not start with A. & D. (the easy answers) and plug them in for your variables and test them.

I started with A and what do you know - it checks out!

{5x+4y=-14}   Put -6 in for x and 4 in for y

-30 + 16 = -14 Is that right? Yes Now try the next equation.

{3x+6y=6}    Put -6 in for x and 4 in for y

-18 + 24 = 6 Is that right? Yes. We are good. Problem solved.

The long way would be to use the substitution method and solve for x and then substitute to find y.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.