Math solutions to two-equation systems

What is the solution of the system? Use a graph. y= -3x + 2 y = -3 x +4|

Answer: no solution See graph. The blue line is the first equation, the purple line is the second. Note that if y = ax + b and "a" is the slope, and b is where the line crosses the y axis (when x=0) the two lines have the same slope (=-3) and are therefore paralell

What is the solution of the system? Use eliminate 3x + 3y = 21 4x + 9y = 48

answer: (3,4) ------------------------------- 3x + 3y = 21 4x + 9y = 48 to make 3y subtractable from 9y, multiple both sides of first equation by -3 -3(3x + 3y = 21) 4x + 9y = 48 -9x + -9y = -63 4x + 9y = 48 add the terms -9x + 4 x = -5x -9y + 9y = 0 -63 + 48 = -15 -5x + 0 = -15 -5x = -15 x = 3 substitute into one of the equations to get x 3x + 3y = 21 3(3) + 3y=21 9 + 3y=21 3y=12 y=4 so, x=3, y = 4

What is the solution of the system? Use substitution. x-y = -6 6x - 3y = -9

answer: (3,9) x-y = -6 6x - 3y = -9 x-y = 6,, then x= y-6 substitute equation for x into second equation 6x - 3y = -9 6 (y-6) - 3y = -9 6y - 36 - 3y = -9 6y - 3y = 36-9 3y = 27 y = 9 go back to one of the equations x - y = -6 x - 9 = -6 x = -6 + 9 x = 3 so, 3,9