-5x +6y = 12 y=5/6x + 2

Question

i need help on this problem by using elimination.

Answer 1

As written the equations look ambiguous.

It may mean two separate equations, which are actually the same

1) -5x + 6y = 12 add 5x to both sides to get

6y = 5x +12 divide by sides by 6 to get

y =5x/6 + 12/6, simplify the constant term

y=5x/6 + 2

that's the same, identical to the 2nd equation

2) y = 5x/6 + 2

the two equations are linearly dependent. They are the same straight line graphically, with an infinite number of solutions, such as (0,2) (6, 7), (12, 12), (18, 17), (24, 22), ...

BUT if somehow you meant to write -5x +6y =12y = 5x/6 +2

then there is a unique real solution (2/13, -12/65)

-5x +6y = 12y

-5x = 6y

x = -6y/5

5x/6+2 = 12y

(5/6)(-6/5)y + 2 = 12y

-y + 2 = 12y

13y = 2

y=2/13

x=-(6/5)y

x= -(6/5)(2/13) = -12/65

(x,y) = (-12/65, 2/13) = about (-0.18, 0.15)

check the solutions, plug in the values for x and y, for each equation

-5x +6y = 12y

-5(-12/65) + 6(2/13) = 12(2/13)

12/13 +12/13 = 24/13

24/13 = 24/13

5x/6 + 2 = 12y

(5/6)(-12/65) + 2 = 12(2/13)

-2/13 + 26/13 = 24/13

24/13 = 24/13

or you could solve this problem graphically

plot -5x +6y = 12y

which in slope intercept form is: y = (-5/6)x with slope = 5/6 and intercept = 0

that's a line through the origin with close to -45 degree angle with the x axis, slightly less than -45.

plot 5x/6 + 2 = 12y

y = (5/72)x + 1/6, slope = 5/72 = nearly a flat line, slightly more than horizontal. intercept = 1/6

the lines intersect about (-1/6, 1/6) slightly less than l-1/6l = 0.16 that's a rough approximation but very close to (-0.18, 0.15), a closer approximation

It helps to graph it to see if your answer is in the right "neighborhood." in the "ball park" even if the graph is just a rough sketch.