Question

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

Answer 1

Answer:

B

Step-by-step 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:

$\frac{1}{3}x + y -4 = 0\\\frac{1}{3}x + (-2x+7) -4 = 0\\\frac{1}{3}x-2x+7-4=0\\\frac{5}{3}x=3\\x=\frac{9}{5}$

Now, y would be:

$y=-2x+7\\y=-2(\frac{9}{5})+7\\y=3\frac{2}{5}$

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