The equations in the system below are parallel.
y = 3 x + 5. y = 3 x + 8
How many solutions does the system have?
no solution
one unique solution
two solutions
an infinite number of solutions
no solution
The graph for the equation y = negative x + 2 is shown below.
On a coordinate plane, a line with positive slope goes through (0, 2) and (2, 0).
If another equation is graphed so that the system has an infinite number of solutions, which equation could that be?
y = negative 2 (x minus 1)
y = negative (x + 2)
y = negative one-fourth (4 x minus 8)
y = negative one-half (x + 4)
y = negative one-half (x + 4)
Consider the equation 6 x + 3 y = 9. Which equation, when graphed with the given equation, will form a system with infinitely many solutions?
y + 2 x = 3
y + 2 x = 9
y = 2 x + 3
y = negative 2 x + 9
y = 2 x + 3
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
line a and line b
Consider the system of equations shown below.
y = negative 5 x + 1. y = negative 5 x + 10
When graphed, the system consists of two lines that will never meet, no matter how far they are extended. Why are the lines parallel?
The linear equations have the same slope and y-intercept.
The linear equations have different slopes and y-intercepts.
The linear equations have the same slope but different y-intercepts.
The linear equations have different slopes but the same y-intercept.
The linear equations have the same slope but different y-intercepts.
To determine the number of solutions for the given system of equations, we need to compare the slopes of the two equations.
The equation of the form y = mx + b represents a line, where m is the slope of the line.
In the given system, both equations have a slope of 3x. Since the slopes of the two equations are the same, the lines they represent are parallel.
When two lines are parallel, they never intersect, which means they have no common point of intersection. So, the system of equations has no solution.
Therefore, the answer is: no solution.