The given system of equations is:
8x - 6y = 48 (equation 1)
8x + 6y = 48 (equation 2)
To find the number of solutions, we need to determine if the two equations represent parallel lines, coinciding lines, or intersecting lines.
Let's simplify the equations to determine their slopes:
Equation 1 can be rearranged to solve for x:
8x = 6y + 48
x = (6/8)y + 6
So, the slope of Equation 1 is 6/8, which can be simplified to 3/4.
Equation 2 can also be rearranged to solve for x:
8x = -6y + 48
x = (-6/8)y + 6
The slope of Equation 2 is -6/8, which can be simplified to -3/4.
Since the slopes of the two equations are different (3/4 and -3/4), the equations represent two intersecting lines. Therefore, the system of equations has exactly one solution.
How many solutions does the system of equations have?
8x−6y=48
8x+6y=48 (1 point)
1 answer
1 answer