a.
1. y = 5x - 4
2. y = -2x + 3
3. y = 3x + 1
4. y = 3x + 1 (Dividing by 2 to get y alone)
5. y = 5x + 2 (Adding 5x to both sides)
6. y = 4x - 1 (Subtracting 1 from both sides)
7. y = 5x
b. Based on the equations above, we can see that they are all in the format y = mx + b.
c. Next, we will pair the equations in order to solve for x and y.
1 & 2:
5x - 4 = -2x + 3
7x = 7
x = 1
Substitute x = 1 into equation 1:
y = 5(1) - 4
y = 5 - 4
y = 1
Equation 1 and 2 have a unique solution (1, 1).
3 & 4:
3x + 1 = 3x + 1
These equations are the same, so they have infinite solutions.
5 & 6:
5x + 2 = 4x - 1
x = -3
Substitute x = -3 into equation 5:
y = 5(-3) + 2
y = -15 + 2
y = -13
Equation 5 and 6 have a unique solution (-3, -13).
7. This equation is y = 5x, representing a line with an infinite number of points and thus infinite solutions.
Therefore, based on the pairs of equations compared:
1. Equation 1 and 2 have one solution.
2. Equation 3 and 4 have infinite solutions.
3. Equation 5 and 6 have one solution.
4. Equation 7 has infinite solutions.
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.
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
7. Y=5x
1 answer