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How many solutions does the system have

How many solutions does the system have-example-1

1 Answer

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Answer:

1 solution

Explanation:

A solution to a system of equations is a point where the equations intersect — in other words, where their x and y values are the same.

In the given system:


\begin{cases} y=-x+5 \\ y=3x+5 \end{cases}

we can see that both equations are written in slope-intercept form:


y=mx+b

where
m is the slope of the line and
b is the y-intercept.

We can see that both equations have a y-intercept at 5; therefore, the solution to the system is at (0, 5).

We can deduce that there are no other solutions because the lines have different slopes; therefore, they will not intersect at any other point.

So, the system of equations


\begin{cases} y=-x+5 \\ y=3x+5 \end{cases}

has 1 solution.

How many solutions does the system have-example-1
User Vibhutha Kumarage
by
8.6k points

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