Can someone please explain? I don't understand

The graph shows two lines, Q and S.

A coordinate plane is shown with two lines graphed. Line Q has a slope of one half and crosses the y axis at 3. Line S has a slope of one half and crosses the y axis at negative 2.

How many solutions are there for the pair of equations for lines Q and S? Explain your answer.

A solution for a pair of lines means that they are equal to each other. This occurs when they instersect. Since the lines have the same slope, but are not the same line, they are parallel, so they will never intersect. This means there are zero solutions.
Hope this helps!

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PratikshaS PratikshaS · Answer 2 · 2022-05-25T13:36:37+02:00

There are no solution for the given pair of equations for the lines Q and S

What is Slope of a line?

Numerical measure of a line's inclination relative to the horizontal

What is Parallel lines?

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect

Given,

Line Q has a slope of one half and crosses the y axis at 3

Therefore,

x=0 and y= 3

Equation of a straight line y= mx + c

where m is slope of the line

Substitute the values in this equation

y= mx + c

3=[tex]\frac{1}{2}[/tex]×0+c

3 = c

y=[tex]\frac{1}{2}[/tex] x + c

Line S has a slope of one half and crosses the y axis at negative 2

Therefore the c will -2

Then the equation of the line y =[tex]\frac{1}{2}[/tex] x - 2

Plot the graph using the equation

So,

both the line Q and S are parallel lines

Therefore there is equation because it wont intersect

Hence, There are no solution for the given pair of equations for lines Q and S

Learn more about Slope of the line and parallel lines here

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