Solving Systems of Equations

Substitution Method:

A solution of a system of equations is an ordered pair that satisfies each equation in the system. To check if an ordered pair is a solution to a system, substitute the number for x and y and see if they equal eachother.

example-

{2x+y=5

{3x-2y=4

(2,1)

2(2)+1=5 3(2)-2(1)=4

5=5 4=4

The ordered pair is a solution

Solving a System of Equations:

example-

{x+y=4 equation 1

{x-y=2 equation 2

Solve equation 1 for y.

y= 4-x

Substitute (4-x) into equation 2 for y.

x-y=2

x-(4-x)=2

x-4+x=2

2x=6

x=3

Solve for y by substituting x=3 into the equation y=4-x

y=4-x

y=4-3

y=1

The solution is the ordered pair of (3,1).

Check in equation 1.

x+y=4

3+1=4

4=4

Check in equation 2.

x-y=2

3-1=2

2=2

Solving a System of Equations by Graphing

example-

{y=lnx

{x+y=1

(1,0) is the only point of intersection on the graph, therefore it is the only solution.

Check.

0=ln1

1+0=1