Question

My answer is D
Solve the following system of equations by graphing.

x + 2y = 4
2x + 4y = 8

What is the solution?

(4,2)
no solution
infinite solutions
none of the above

Answer 1

nope

Answer 2

first of all, "none of the above" makes no sense in this context
you have to equations for lines
they either intersect (one solution)
they are parallel (no solution)
or they are the same line (infinitely many solutions)

it has to be one of those three

Answer 3

if you multiply both sides of the first equation by 2, you get the second equation exactly
that means they are the same line

Answer 4

make sure it is clear to you that although the equations
\[x+2y=4\] and \[2x+4y=8\] look different, they are actually the same equation

Answer 5

check for example that any point on the first line is also on the second, and vice versa
that means there are infinitely many solutions

Answer 6

I got "infinite solutions"

Answer 7

yup

Answer 8

which is another way of saying any \((a,b)\) that satisfies the first equation also satisfies the second, and the other way around