Classify each system without graphing: 3x-2y=8, 4y=6x-5

Question

3x-2y=8, 4y=6x-5

2x+8y=6, x=-4y+3

Answer 1

Linear system is 3x - 2y = 8 and 4y = 6x - 5

Slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

Write the above equations in to slope intercept form.

First equation is 3x - 2y = 8

- 2y = - 3x + 8

Divide each side by negative 2.

y = (3/2)x - 4

Compare it to y = mx + b.

Slope = 3/2, y intercept  = - 4

 Second equation 4y = 6x - 5

Divide each side by 4.

(4y/4) = (6x/4) - (5/4)

y = (3/2)x - (5/4)

Slope = 3/2, y intercept  = - 5/4

Observe the two lines slopes are equal.

We know that parallel lines slopes are equal to each other.

Therefore, the system of equations are parallel lines.

The lines does not intersect.

There is no solution.

Answer 2

Linear system is 2x + 8y = 6 and x = - 4y + 3

Slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

Write the above equations in to slope intercept form.

First equation is 2x + 8y = 6

 8y = - 2x + 6

Divide each side by 8.

8y/8 = (-2/8)x + 6/8

y = (-1/4)x + 3/4

Compare it to y = mx + b.

Slope = -1/4, y intercept  = 3/4.

 Second equation x = - 4y + 3

x - 3 = - 4y

Divide each side by negative 4.

(- 4y/-4) = x/(-4) + (-3)/(-4)

y = (-1/4)x + 3/4

Slope = -1/4, y intercept  = 3/4

Observe the two lines are same.

Therefore, the system of equations are infinitly many solutions.