Question

How many solution does this system have?
2x+y=3
6x=9-3y
A. 1
B. 0
C. Infinite
D. 2

Answer 1

\(\large\color{slate}{\displaystyle 2x+y=3 }\)

\(\large\color{slate}{\displaystyle \color{red}{(}2x+y=3\color{red}{)\times 3} }\)

\(\large\color{slate}{\displaystyle \color{red}{(}2x\color{red}{)\times 3}+\color{red}{(}y\color{red}{)\times 3}=\color{red}{(}3\color{red}{)\times 3} }\)

\(\large\color{slate}{\displaystyle 6x+3y=9 }\)

\(\large\color{slate}{\displaystyle 6x+3y\color{red}{-3y}=9 \color{red}{-3y}}\)

\(\large\color{slate}{\displaystyle 6x=9 -3y}\)

Answer 2

So your first equation is really the same as the second equation.

Answer 3

so 2 is my answer?

Answer 4

Every point on a line is a solution to the equation of the line. A single line has an infinite number of solutions because there is an infinite number of points that satisfy the equation of the line.

If two lines are parallel, then the system of equations formed by those lines has no solution because there is no point that satisfies both lines.

If two lines intersect at one point, then that single point is the solution of the system of equations created by the equations of the two lines.

If you are given a system of equations, and it turns out that both equations are the same equation, then you really only have one equation. How many solutions does a single equation have?