Imagine that you are given two linear equations in slope-intercept form. you notice that the slope of both equations is the same, and the y-intercept for both equations is also the same. solve for the number of solutions you would expect for this system of equations.

a. 1
b. infinitely many
c. 0
d. cannot be determined

When two equations have same slope and their y-intercept is also the same, they are representing the line. In this case one equation is obtained by multiplying the other equation by some constant.

If we plot the graph of such equations they will be lie on each other as they are representing the same line. So each point on that line will satisfy both the given equations so we can say that such equations have infinite number of solutions.

Consider an example:

Equation 1: 2x + y = 4

Equation 2: 4x + 2y = 8

If you observe the two equation, you will see that second equation is obtained by multiplying first equation by 2. If we write them in slope intercept form, we'll have the same result for both as shown below:

Slope intercept form of Equation 1: y = -2x + 4

Slope intercept form of Equation 2: 2y = -4x + 8 , ⇒ y = -2x + 4

Both Equations have same slope and same y-intercept. Any point which satisfy Equation 1 will also satisfy Equation 2. So we can conclude that two linear equations with same slope and same y-intercept will have an infinite number of solutions.

Therefore the correct answer is option B.

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