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
The equation y = negative 5 x + 10, when graphed with y = 5x - 10, will form a system with no solution. This is because the slopes of the two lines are opposite in sign, meaning they are parallel and will never intersect.
choose an awnser for the previous question
y = negative 5x + 10.
The graph for the equation y = 2 x + 4 is shown below.
On a coordinate plane, a line goes through (negative 2, 0) and (0, 4).
If another equation is graphed so that the system has one solution, which equation could that be?
y = 2 x minus 4
y = 2 (x + 2)
y = 2 (x minus 4)
y = x + 4
choose an awnser
The equation y = 2 (x - 2) can be graphed with the given equation and will form a system with one solution. This is because the two lines intersect at point (-2, 0), giving a unique solution to the system.
incorrect
I'm sorry about that. Let me explain.
The slope of the line passing through (-2, 0) and (0, 4) is (4 - 0) / (0 - (-2)) = 2. Therefore, the line passing through (-2, 0) and (0, 4) has an equation y = 2x + 4.
For the system to have exactly one solution, the other line must pass through a point that does not lie on the line y = 2x + 4 and has a slope different from 2. The equation y = 2(x - 1) satisfies these conditions and will form a system with one solution.
So, the answer is y = 2(x - 1). I apologize for the confusion caused earlier.
still incorrect would you like awnser choices
I apologize again for the confusion. Please provide answer choices, so I can accurately choose the correct answer.
y = 2 x minus 4
y = 2 (x + 2)
y = 2 (x minus 4)
y = x + 4
The equation y = 2 (x + 2) can be graphed with the given equation and will form a system with one solution. This is because the two lines intersect at point (-2, 0), giving a unique solution to the system.
Therefore, the answer is y = 2 (x + 2).