Question

What is the solution to the system below?
2x+y=3
4x+2y =9


(2, 2)

(2, -2)

no solution

infinite solutions on the line

Answer 1

Do you prefer elimination or substitution?

Answer 2

elimination

Answer 3

All right, try multiplying each term in the first equation by -2 and add to the other equation.

Answer 4

not sure what you mean

Answer 5

To eliminate one of the variables, we can multiply each term in one of the equations that will make a variable cancel out when you add them. If you multiply both sides of the first equation by -2, you get\[-2(2x+y)=-2(3)\]\[-4x-2y=-6\]Now we can add the new equation to the second one. This gives us 0=3. Because it gives us a false statement, it means that there is no solution to the system. If you graph each line in y=mx+b form, you will see that they are parallel lines. This means they never intersect which implies there is not value of x and y where they are equal.

Answer 6

oh. I see now.

Answer 7

Great =)