Question

Question 1
Examine the six different equations that follow:
1. y=5x–4
2. y=–2x+3
3. y=3x+1
4. 2y=6x+2
5. y–5x=+2
6. y–4x+1=0
Complete steps a. through e. to determine which pair of equations form a system
with one solution, no solution, or infinite solutions.
a. Solve each equation and make sure it is in y=mx+b format

Answer 1

what ones have no solution, one solution, or infinite solutions

Answer 2

you need to solve those equations

Answer 3

1. y = 5x - 4 (already in y=mx+b format)

2. y = -2x + 3 (already in y=mx+b format)

3. y = 3x + 1 (already in y=mx+b format)

4. 2y = 6x + 2
Divide both sides by 2 to isolate y:
y = 3x + 1 (now in y=mx+b format)

5. y - 5x = 2
Add 5x to both sides to isolate y:
y = 5x + 2 (now in y=mx+b format)

6. y - 4x + 1 = 0
Subtract 4x and 1 from both sides to isolate y:
y = 4x - 1 (now in y=mx+b format)

Now all the equations are in y=mx+b format.

Answer 4

To determine which pair of equations have no solution, one solution, or infinite solutions, we need to compare their slopes and y-intercepts.

1. Equation: y = 5x - 4
Slope (m): 5
Y-intercept (b): -4

2. Equation: y = -2x + 3
Slope (m): -2
Y-intercept (b): 3

3. Equation: y = 3x + 1
Slope (m): 3
Y-intercept (b): 1

4. Equation: y = 3x + 1
Slope (m): 3
Y-intercept (b): 1

5. Equation: y = 5x + 2
Slope (m): 5
Y-intercept (b): 2

6. Equation: y = 4x - 1
Slope (m): 4
Y-intercept (b): -1

Now let's compare the equations:

- Equations 1 and 4 have the same slope and same y-intercept. They represent the same line, so they have infinite solutions.

- Equations 2, 3, 5, and 6 have different slopes and different y-intercepts. They represent different lines, so each pair of equations has one solution.

Answer 5

Apologies for misunderstanding your request. Let's solve each equation to determine the solutions.

1. y = 5x - 4
To find the solution, we need another equation to form a system. Let's move on to the next equation.

2. y = -2x + 3
Again, we need another equation to form a system.

3. y = 3x + 1
Similar to the previous equations, we need another equation to solve the system.

4. 2y = 6x + 2
Divide both sides by 2:
y = 3x + 1

Now we have two equations to form the system:
y = 5x - 4
y = 3x + 1

To find the solution, we can set them equal to each other:
5x - 4 = 3x + 1

Subtract 3x from both sides:
2x - 4 = 1

Add 4 to both sides:
2x = 5

Divide both sides by 2:
x = 2.5

Now, substitute x back into either equation to find y:
y = 3(2.5) + 1
y = 7.5 + 1
y = 8.5

Therefore, the solution to the system of equations is x = 2.5 and y = 8.5. This system has one solution.

Let's continue with the other equations to find their solutions.

5. y - 5x = 2
Solve for y in terms of x:
y = 5x + 2

Again, we need another equation to form a system.

6. y - 4x + 1 = 0
Rearrange the equation:
y = 4x - 1

Similarly, we need another equation to form a system.

Based on the given equations, only equation 4 (2y = 6x + 2) and equation 3 (y = 3x + 1) form a system with one solution. The other equations either require additional equations to form a system or have no solution.