Question

Are these parallel or perpendicular or neither? 3x+2y=10 and 2x+3y=-3

Answer 1

The given equations 3x + 2y = 10 and 2x + 3y = -3 do not represent parallel or perpendicular lines.

Step-by-step explanation:

The given equations are 3x + 2y = 10 and 2x + 3y = -3. To determine if these equations represent parallel lines, perpendicular lines, or neither, we can compare their slopes. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope. So, let's rearrange the given equations in slope-intercept form:

Equation 1: 3x + 2y = 10 --> 2y = -3x + 10 --> y = (-3/2)x + 5

Equation 2: 2x + 3y = -3 --> 3y = -2x - 3 --> y = (-2/3)x - 1

We can see that the slopes of the two lines are different: -3/2 and -2/3. Since the product of these slopes is not -1, the lines are not perpendicular. Additionally, the lines are not parallel because their slopes are not equal. Therefore, the given equations represent neither parallel nor perpendicular lines.

Answer 2

These lines are neither parallel nor perpendicular.

Step-by-step explanation:

Parallel lines are lines that never intersect and perpendicular intersect at a ninety degree angle.

Using desmos, you can find your solution.

I hope this helps

-No one