1. ## Linear systems?

Show whether (0, 3) is the solution of the linear system below:
2x+y=-3
X+2y=8

How would you do this?

2. (0,3) is the point so you want to see if this point is on the lines given. Here 0 is your x coordinate and 3 is your u coordinate
You simply fill 0 and 3 wherever there is an x and y respectively in the line equations and if the line is = 0 then it is the linear solution

4. Substitute x = 0 and y = 3 in the first equation.

$\displaystyle 2x + y = -3$

$\displaystyle 2(0) + 3 = -3$

$\displaystyle 0 + 3 = -3$

$\displaystyle 3 = -3$

Because three does not equal the opposite of three, the equation $\displaystyle 3 = -3$ is false. Therefore, the point (0,3) is not a solution to the system of linear equations.

If the equation were true, then substitute x = 0 and y = 3 in the second equation. If that equation were true, then the point (0,3) would be a solution of the system of linear equations.

In general, substitute (x,y) in each equation of the system. If the substitution produces an invalid equation, then the point (x,y) is not a solution to the system of equations. If the substitution produces a valid equation, then the point (x,y) is a solution to the system of equations.