Question

How many solutions does the system of equations below have?
y=5/6x-2
y=-2/5x+3/7

Answer 1

One solution [at (1.97,-0.4)]

Explanation:

Both equations are straight line. They do not have the same slope [(5/6) and (2/5)], so they will intersect at some point on a two dimensional graph.

Out of curiosity, we can find the solution:

y = (5/6)x-2

y = -(2/5)x+3/7

We can set them equal to each other, since y = y:

(5/6)x-2 = -(2/5)x+3/7

30*(5/6x-2) = 30*(-(2/5)x+3/7) [Multiply both sides by 30]

25x - 60 = -12x + (90/7)

37x = (90/7) + 60

37x = 12.9 + 60

x = 1.97

Use this value of x to find y:

y = (5/6)x-2

y = (5/6)*(1.97)-2

y = -0.4

The solution is (1.97,-0.4)

See the attached graph.

Answer 2

Answer: 1 solution

Reason: The two lines of the form y = mx+b have different slopes. The "m" is the slope.

The slope of the 1st and 2nd equations are 5/6 and -2/5 respectively. Since the two slopes are different, the lines aren't parallel. The non-parallel lines intersect at exactly one point. This intersection is the solution.