Question

One equation from a system of equations is given to u below

Y-2=4/7(x-5)

Which of the following equations will create a system with no solution

Select two that will apply.

Y=2x-5
Y=4/7x+9
Y+3=2(x-1)
Y-1=4/7(x+3)

Answer 1

To identify a system with no solution, we look for equations that are parallel to the given equation, meaning they have the same slope but different y-intercepts. The answer is the equation that has the same slope as the original equation: Y-1=4/7(x+3).

Step-by-step explanation:

The given equation Y-2=4/7(x-5) can be re-written in slope-intercept form as Y = 4/7x - 4/7 * 5 + 2. To find a system of equations with no solution, we look for another linear equation with the same slope but a different y-intercept. This means the lines are parallel and will never intersect.

The equation Y-1=4/7(x+3) can be transformed into slope-intercept form, yielding Y = 4/7x + 4/7 * 3 - 1. This equation shows the same slope but a different y-intercept from the original equation.

The other options either do not share the same slope or are written in a way that does not provide enough information about their slope without further manipulation:

• Y=2x-5 has a slope of 2.
• Y=4/7x+9 has the same slope but is not written in a way that directly confirms it's a different line without rearranging the equation.
• Y+3=2(x-1) has a slope of 2.

Therefore, the equation that will create a system with no solution is Y-1=4/7(x+3), as it has the same slope but a different y-intercept.