Answer: The number of solutions for the system of linear equations depends on whether the lines are parallel or intersect at a single point. If the lines are parallel, there are no solutions, as they never meet. If the lines intersect at a single point, there is exactly one solution.
To determine the number of solutions, we need to find the point of intersection of the two lines. We can do this by solving for x in one equation and substituting it into the other equation:
2x + 3 = 8/4 x - 1/4
8x + 12 = 2x - 1/2
6x = - 12.5
x = -2.08
Then, substituting this value of x back into either equation to find the corresponding value of y:
y = 2 * (-2.08) + 3 = 0.16
So, the two lines intersect at the point (-2.08, 0.16), which means there is exactly one solution to the system of linear equations.
Explanation: