Question

Which of the following best describes the solution to the system of equations below?

3x + 5y = 9
3x + 5y = 15

Answer 1

Choice D is correct answer.

Explanation:

We have given a system of equations.

3x + 5y = 9 eq(1)

3x + 5y = 15 eq(2)

We have to find the description of the solution of equations.

y = mx+c is the slope-intercept of equation of line where m is slope and c is y-intercept.

Eq(1) can be written as:

y = -3/5x + 3 where slope is -3/5.

Eq(2) can be written as:

y = -3/5x+5 where slope is -3/5.

Equations with equal slopes are of parallel lines and parallel lines have no solution.Hence, system has no solutions.

Choice D is correct answer.

Answer 2

Answer: Option D

Explanation:

The equation of the line in slope intercept form is:

`y=mx+b`

Where m is the slope and b the y-intercept.

Solve for y from both equations:

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

`5y=-3x+15\\y=(-3)/(5)x+3`

As you can see, the slopes of the lines are equal, therefore, they are parallel.

If the lines are parallel then the system of equtions has no solution.