Question

Classify the system of equations 2x + y - 7 = 0 1/3 x + y - 4 = 0

a. coincident
b. intersecting
c. parallel

Answer 1

B

Explanation:

The equations are:

2x + y - 7 = 0

and

1/3x + y -4 = 0

Let's rearrange the first to get:

y = -2x + 7

Putting this into the 2nd equation we get:

`(1)/(3)x + y -4 = 0\\(1)/(3)x + (-2x+7) -4 = 0\\(1)/(3)x-2x+7-4=0\\(5)/(3)x=3\\x=(9)/(5)`

Now, y would be:

`y=-2x+7\\y=-2((9)/(5))+7\\y=3(2)/(5)`

Solving the equation we see that there is 1 unique solution with 1 x value and another y values. That means, when graphing, the lines would intersect.

Answer choice B is right.

Note: Coincident means the same line and parallel means there would be no solution when solving