The graph for the equation y = x minus 4 is shown below.
On a coordinate plane, a line goes through (0, negative 4) and (4, 0).
Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
y minus x = negative 4
y minus x = negative 2
y minus 4 = x
y + 4 x = 1
The equation y + 4x = 1 will form a system with y = x - 4 that has an infinite number of solutions. To see why, we can substitute y = x - 4 into the equation y + 4x = 1 to get (x-4) + 4x = 1, which simplifies to 5x - 4 = 1, or 5x = 5, or x = 1. Substituting x = 1 into y = x - 4 gives y = -3. So the solution to the system is (1, -3), and any equation that passes through this point will also intersect y = x - 4 at that point, giving an infinite number of solutions.
choose a awnser for the previous question
The equation y + 4x = 1.
The graph for the equation y = negative 2 x + 1 is shown below.
On a coordinate plane, a line with negative slope goes through (0, 1) and (1, negative 1).
If another equation is graphed so that the system has no solution, which equation could that be?
y = negative 2 (x minus one-half)
y = negative one-half (4 x + 2)
y = negative x + 1
y = negative one-half x + 2
The equation y = -x + 1 can be graphed with the given equation and will form a system with no solution. This is because the slope of y = -x + 1 is opposite in sign to the slope of y = -2x + 1, which means the lines will never intersect and there is no solution to the system.
choose a awnser for the previous question
y = -x + 1.
A system of equations is shown on the graph below.
On a coordinate plane, 2 lines intersect at (negative 1, 2).
How many solutions does this system have?
no solutions
one unique solution
two solutions
an infinite number of solutions
This system has one unique solution.
The graphed line shown below is y = 5 x minus 10.
On a coordinate plane, a line goes through (2, 0) and (3, 5).
Which equation, when graphed with the given equation, will form a system that has no solution?
y = negative 5 x + 10
y = 5 (x + 2)
y = 5 (x minus 2)
y = negative 5 x minus 10