Solving Systems of Linear Equations
Solving Systems
of Equations
by Graphing
Example: Solve the system of
equations by graphing:
x - 2y = 1
x + y = 4
Solve each for y:
y = ½x - ½
y = -x + 4
Solving Systems
of Equations
Algebraically
Example: Solve by substitution:
3x + 6 = 7y
x + 2y = 11
Solve one for
either variable:
x = 11-2y then substitute (11-2y) in for x in the other equation:
3(11-2y) + 6 = 7y
33 - 6y + 6 = 7y
39 = 13y
3 = y
x = 11-2(3)
x = 5
Point of intersection is (5,3)
Example: Solve by elimination:
x- 2y = 0
y = 2x - 3
Arrange the
equation in standard form:
x-2y = 0
-2x + y = -3
Multiply bottom equation by 2 to cancel out ys:
x - 2y = 0
-4x + 2y = -6
then combine like terms to find x
-3x = -6
x = 2
2 - 2y = 0
-2y = -2
y = 1
the point of intersection is (2,1)
Application of Systems of Equations:
If the Astros sold 15 hats and 12 shirts the first hour of the game and made $364.50. Then sold 10 hats and 9 shirts and made $255.25. How much was each hat and each shirt?
x = hats and y = shirts
15x + 12y = 364.50
10x + 9y = 255.25
Use elimination by multiplying
top equation by -3 and bottom by 4
-45x - 36y = -1093.5
40x +36y = 1021
the y coordinate cancels then combine the x and constant
-5x = -72.5
x = 14.50
plug x back in to either equation to get y
10(14.5) + 9y = 255.25
145+ 9y = 255.25
9y = 110.25
y = 12.25
therefore hats costs $14.50 and shirts costs $12.25
Click here for more REVIEW MATERIAL
Click here for more APPLICATION PRACTICE
Graphing Systems of Inequalities
y > x - 2
y < -2x + 4
Graph each and shade
appropriate area:
Example Problems
1. Solve the system by graphing: x +
y = 5
2x - y = 4
2. Solve the system using
substitution: 5x + 3y = -4
7x - y = 36
3. Solve the system using
elimination: 2x - y = 4
2x + 3y = 12
4. Solve the system using either
method: x + y = 6
3x - 4y = 4
5. Graph the inequality:
y ³ -x +
5
y> 1½x - 5