Write a system of linear equations represent by the graph

inequality 1:

inequality 2:

From graph,

inequality 1:  y > x+(-2)

inequality 2: y > (-4)x+2

Step-by-step explanation:

The graph shows two lines on the X-Y plane.

Step 1: Find the equation of a line.

From figure, One line is passing through (3,0) and (0,-2)

Slope of line is given by m=

m=

m=

Y-intercept isc=(-2)

The equation of line is given by y=mx+c

Therefore, y=x+(-2)

From figure, Another line is passing through (0.5,0) and (0,2)

Slope of line is given by m=

m=

m=

m=(-4)

Y-intercept isc=(2)

The equation of line is given by y=mx+c

Therefore, y=(-4)x+2

Step 2: Test of origin and finding inequality

For y=x+(-2)

Let suppose,  y > x+(-2)

This line is shaded toward the origin then, inequality must satisfy the origin

Test for origin says,

0 > (0)+(-2)

0 > (-2)

TRUE.

y > x+(-2) is required inequality

For y=(-4)x+2

Let suppose, y > (-4)x+2

This line is shaded away from the origin then, inequality must not satisfy the origin

Test for origin says,

0 > (0)+(-2)

0 > (+2)

FALSE, so that y > (-4)x+2 does not satisfy the origin

y > (-4)x+2 is required inequality

Thus,

inequality 1:  y > x+(-2)

inequality 2: y > (-4)x+2

option a is correct.

only one solution to the system of equations

step-by-step explanation:

if the graph of the equations do not intersects(i.,e if they are parallel) then, there are no solutions that are true for both the equations.

if the graph of the equations intersects, then there is one solution and that is true for both the equations.

since, in the given figure:

the two lines intersect each other

⇒there is only one solution which satisfy both the lines of an equations.

therefore, there is only one solution to the system of equation