Consider the graph with four lines below. On a coordinate plane, line a has a positive slope and goes through points (negative 1, 0) and (1, 2), line b has a negative slope and goes through (negative 2, 2) and (negative 1, negative 1), line c has a negative slope and goes through (0, 3) and (1, 0), and line d is horizontal at y = 1. By inspection, which system would have no solution? line a and line b line a and line c line b and line c line b and line d

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The system of equations that do not have any solution is line b and line c. Hence, the correct option is C.

What is the equation of a line?

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The equation of line a passing through (-1,0) and (1,2) are,

m = (0-2)/(-1-1) = -2/-2 = 1

y= x + c

0 = -1 + c

c = 1

Equation of line 1, y=x+1

The equation of line b passing through (-2,2) and (-1,-1) are,

m = (2+1)/(-2+1) = 3/-1 = -3

y= -3x + c

-1 = -3(-1) + c

c = -4

Equation of line 1, y=-3x-4

The equation of line c passing through (0,3) and (1,0) are,

m = (3-0)/(0-1) = 3/-1 = -3

y= -3x + c

3 = -3(0) + c

c = 3

Equation of line 1, y=-3x+3

Also, the equation of line d is y=1

The solution of two-equation is the point at which the two equations are not intersecting. Therefore, the system of equations that do not have any solution is line b and line c.

Hence, the correct option is C.

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