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
Step a. Solve the equation:
1. y = 5x - 4
This equation is already in y = mx + b format.
Step b. Determine the slope (m) and y-intercept (b) of the equation:
The slope (m) is 5 and the y-intercept (b) is -4.
Now let's move on to the next equation:
2. 3y = 15x - 12
Step a. Solve the equation:
To get the equation in y = mx + b format, divide both sides by 3:
y = (15/3)x - 12/3
Simplifying the equation further,
y = 5x - 4
Step b. Determine the slope (m) and y-intercept (b) of the equation:
The slope (m) is 5 and the y-intercept (b) is -4.
Since both equations have the same slope (m) and y-intercept (b), they represent the same line. Therefore, the pair of equations form a system with infinite solutions.
To solve equation 1, we rearrange it into y = mx + b format:
y = 5x - 4.
Now let's look at the other equation(s) to determine if they form a system with one solution, no solution, or infinite solutions. Could you please provide the other equation(s) in the system?
To determine which pair of equations form a system with one solution, no solution, or infinite solutions, we need to have another equation to compare with the given equation y=5x-4.
b. Let's consider the equation 2y=10x+6 and solve it for y:
2y = 10x + 6
Divide both sides by 2 to isolate y:
y = 5x + 3
c. Now we have two equations:
1. y = 5x - 4
2. y = 5x + 3
d. By comparing the equations, we can see that the coefficients of x are the same (both are 5) but the constant terms (the numbers without x) are different (-4 and +3).
e. Since the coefficients of x are the same but the constant terms are different, the two equations form a system with one solution. This is because the lines represented by the equations are parallel and will never intersect, except at one point where they coincide.