Question

Determine the number of solutions you will have for the system 2x + y = 8 and 2y = 4x + 1.
A) Infinite solutions
B) One solution
C) Impossible to determine
D) No solution
and can u explain

Answer 1

I would start by getting both of these equations in y= form. This will help us visualize the graphs. For the first equation we just need to subtract 2x from both sides:
y=-2x+8
For the second one we just need to divide by two:
y=2x+(1/2)

These lines have different slopes. This means they aren't the same line (so infinite solutions is incorrect) and aren't parallel (so no solutions is also incorrect). Any two lines that have different slopes will intersect exactly once. So there will be 1 solution.