Question

Do you know the answer?

Answer 1

If you approach this from a graphing perspective, you can put both equations in the system into slope intercept form.

System A:

Line 1: 3x + 5y = 8

5y = -3x + 8

y = -3/5 x + 8/5

Line 2: 3x + 5y = 7

5y = -3x + 7

y = -3/5 x + 7/5

Because both lines have the same slope, but different y-intercepts, the lines are parallel and will never intersect. This is why there is no solution to the system.

System B:

Line 1: y = 7x is in slope intercept form.

Line 1: y = 3x is in slope intercept form.

Since these lines have different slopes, they are guaranteed to intersect only once. There is a single solution.

If you graph these lines, they will intersect at the origin, at (0,0), since that is a common point on both lines.

Answer 2

A. No Solution

B. Unique Solution (0,0)

Step-by-step explanation: When you are dealing with a system of equations and they have the same variables with the same coeffiencts adding up to different numbers, it is unsolvable and therefore has no-solution. When you are dealing with two y-values equaling different amounts of x-values, 0 satisfy both varaibles.