Systems of EquationsA group of two or more equations is called a

system.When asked to SOLVE a system of equations, the goal is to find a single ordered pair (x, y) that makes ALL the equations true.

So if y = f(x) and y = g(x), then the solution(s) will be where f(x) = g(x)

Example: What is the solution to the system below?

3x + 2y = 1y – 2x = 11

To solve a system of equations you can use algebra.

Process:a) Rewrite both equations so it’s

y =...b) Set the two expressions with

x, equal to each otherc) Solve the new equation for x.d) Substitute that answer into

one of the ORIGINAL equations to find the matching y.

Example:3x + 2y = 1y – 2x = 11

System with a Linear and a Quadratic function

Example:

1) Set both equation to y = …2) Set the expressions with x equal to each other.3) Solve the resulting quadratic equation for x4) Substitute x into linear equation to find matching y.

You Try…

1) 3x + 2y = 9 x – 3y = 3

2) y = 2x2 – 5x – 3 y = x + 5

Another way to solve systems of equations is by graphing.

2x + y = 9y – 3x = -4

Process:

1)Write each equation into y =… form

2)Graph the functions either by hand or on calculator

3)The point where the two lines cross is called the point of intersection.

This is the solution (x,y) to the system of equations. This is where f(x) = g(x).

Graphing functions on the calculator1.  Change equations into y = … form2. Enter the first equation into Y1.3. Enter the second equation into Y2.4. Hit GRAPH. (change window if needed so you can see the graphs cross)5.  Use the INTERSECT option to find the solution:     2nd TRACE (CALC) #5 intersect     Move spider (using arrows) close to the intersection.     Hit ENTER 3 times.                                                    

Try another… solve the system by graphing

y = 2x2 – 5x – 3

y = x + 5

If the functions do not intersect, then there is no solution.

For 2 linear functions, if the lines create a single line (one on top of the other), then there are infinite solutions.