A system of equations has 1 solution. If 4x−y=5 is one of the equations, which could be the other equation?Responsesy=−4x+5y is equal to negative 4 x plus 52y=8x−102 y is equal to 8 x minus 10y=4x−5y is equal to 4 x minus 5−2y=−8x−10
Question
A system of equations has 1 solution. If 4x−y=5 is one of the equations, which could be the other equation?Responsesy=−4x+5y is equal to negative 4 x plus 52y=8x−102 y is equal to 8 x minus 10y=4x−5y is equal to 4 x minus 5−2y=−8x−10
Solution
The other equation could be 2y=8x−10.
Here's why:
The given equation is 4x - y = 5. We can rearrange this to y = 4x - 5.
Now, let's look at the second equation, 2y = 8x - 10. We can rearrange this to y = 4x - 5.
Since both equations are the same, they will intersect at all points, meaning there is only one solution to this system of equations.
The other options won't work because:
- y = -4x + 5: This line has a different slope and y-intercept, so it will intersect the given line at one point, but it will not coincide with it.
- y = 4x - 5: This is the same as the given equation, so it's not a different equation.
- -2y = -8x - 10: This can be simplified to y = 4x + 5, which is a different line from the given equation.
Similar Questions
A system of equations has infinitely many solutions. If 2y−4x=6 is one of the equations, which could be the other equation?Responsesy=4x+6y is equal to 4 x plus 6−y=−4x+6negative y is equal to negative 4 x plus 6y=2x+6y is equal to 2 x plus 6−y=−2x−3
Which system has no solution?Responsesy=9x+6.25−18x+2y=12.5y is equal to 9 x plus 6 point 2 5; negative 18 x plus 2 y is equal to 12 point 5y=3x+9x+8y=12.3y is equal to 3 x plus 9; x plus 8 y is equal to 12 point 3y=4.5x−5−3x+2y=6y is equal to 4 point 5 x minus 5; negative 3 x plus 2 y is equal to 6y=−3x+86x+2y=−4.5
Which of these systems of equations have a solution of (–12,10)? Select all that apply.5x+5y=–10x–y=–22y=–x–2–2x–y=143x+4y=–4y=–4x–36y=–5x–50y=10x=12x+y=–2y=–3x–26y=2x+34Submit
Solve the system: x = y2 + 4y – 5, x = 0.Question 17Select one:a.(0, –5) and (1, 1)b.(4, 4) and (–5, –5)c.(0, 1) and (0, –5)d.No solutione.None of these
-2x + 8y = 4x = 4y + 1These are the last two lines in Isaac's work:-8y - 2 + 8y = -4-2 = 4Assuming Isaac solved the system correctly, which statement best represents the solution to this system?*1 pointy equals -2y equals 4There are infinitely many solutions to this system.There is no solution to this system.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.