Question

Solve the system. 2x + y = 3 −2y = 14 − 6x Write each equation in slope-intercept form. y = x + y = x +

Answer 1

3 equations in slope intercept form: y = -2/3·x + 1 y = -8x + 14 y = 3x - 11/2 Solution: (39/22, -2/11) We have a set of 3 equations, that we can create 3 lines from. So let's do so: 2x + y = 3 â’2y = 14 â’ 6x Line 1: 2x + y = 3 - 2y 2x = 3 - 3y 2x - 3 = -3y -2/3·x + 1 = y y = -2/3·x + 1 Line 2: 2x + y = 14 - 6x y = 14 â’ 8x y = -8x + 14 Line 3: 3 - 2y = 14 â’ 6x -2y = 11 â’ 6x y = -11/2 + 3x y = 3x - 11/2 So the 3 equations are: (1) y = -2/3·x + 1 (2) y = -8x + 14 (3) y = 3x - 11/2 Let's subtract equation (3) from equation (2) and solve for x. y = -8x + 14 y = 3x - 11/2 0 = -11x + 19.5 11x = 19.5 22x = 39 x = 39/22 We now have an X value of 39/22. Let's verify that the y values match. (1) y = -2/3·x + 1 y = -2/3·39/22 + 1 y = -78/66 + 1 y = -13/11 + 1 y = -2/11 (2) y = -8x + 14 y = -8·39/22 + 14 y = -312/22 + 14 y = -156/11 + 14 y = -2/11 (3) y = 3x - 11/2 y = 3·39/22 - 11/2 y = 117/22 - 11/2 y = 117/22 - 121/22 y = -4/22 y = -2/11 And they all match.

Answer 2

y=-2x+3

y=3x+-7

How do the slopes and y–intercepts of the two equations compare? The slopes and the y-intercepts are different.