Question

Which graph shows the solution to the system of linear equations? y equals negative one fourth times x plus 1 y = −2x − 1 a coordinate grid with one line that passes through the points 0 comma 1 and 4 comma 0 and another line that passes through the points 0 comma negative 1 and 1 comma negative 3 a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma 0 and another line that passes through the points 0 comma negative 3 and 1 comma negative 5 a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma negative 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 5 a coordinate grid with one line that passes through the points 0 comma 1 and 4 comma negative 2 and another line that passes through the points 0 comma negative 2 and 1 comma negative 5

Answer 1

Explanation:

The system of linear equations is:

y = -1/4 x + 1

y = -2x - 1

To find the solution to the system, we need to find the point where the two lines intersect. We can do this by graphing the two lines and finding their point of intersection, or by solving the system of equations algebraically.

Using the second method, we can substitute the first equation into the second equation for y:

-1/4 x + 1 = -2x - 1

Simplifying and solving for x, we get:

15/8 x = 2

x = 16/15

Substituting this value of x into the first equation to solve for y, we get:

y = -1/4 (16/15) + 1

y = 19/15

So the solution to the system is (16/15, 19/15).

Looking at the graphs, we can see that only the first option has a point of intersection that matches the solution we found algebraically. Therefore, the graph that shows the solution to the system of linear equations is a coordinate grid with one line that passes through the points 0,1 and 4,0 and another line that passes through the points 0,-1 and 1,-3.