Download Graphing Systems Study Guide (4)

Name _________________________________________________________
RETEACHING
Date ____________________________
6-4
SYSTEMS OF EQUATIONS
A graph can help you solve some systems of equations.
If the graphs of two lines intersect, there is one solution—the point of
intersection.
If the graphs of two lines are parallel, there is no solution.
If the graphs of two lines coincide, there is an infinite number of
solutions—all points on the line.
E x a m p l e
3x 4
y12x
6y 6
Solve the system of equations by graphing.
Solution
Graph each equation. Then read the solution from the graph.
• To graph, write each equation in the slope-intercept form
and identify the y-intercept, b, and the slope, m.
y 3x 4
b 4, m 3
12x 6y 6 ➝ 6y 12x 6 ➝ y 2x 1
b 1, m 2
• Use the y-intercept and the slope to graph each equation.
The lines intersect at the point (3, 5).
So, the solution is (3, 5).
EXERCISES
Solve each system of equations by graphing. Graph Exercises 4–6 on another sheet of
paper.
1.
8
2y2y 3x
2x 2
6
O
4y7x 6x14y 16
6
3.
O
6y 12
3x
2x 4y 8
6
4
4
4
2
2
2
6 4 2 0
4.
2.
2
4
6 4 2 0
6N
2
4
6 4 2 0
6N
2
2
2
4
4
4
6
6
6
x2xy 8y 48
© Glencoe/McGraw-Hill
5.
4
xy 2x
6
186
6.
O
2
4
6N
3x 2
y3x
y 1
MathMatters 3
Name _________________________________________________________
EXTRA PRACTICE
Date ____________________________
6-4
SYSTEMS OF EQUATIONS
EXERCISES
Determine the solution of each system of equations.
1.
4
2.
y
4
2
y
2
x
2
-4
4
-4
2
-2
-2
4x
-2
-4
Solve each system of equations by graphing. Use your own paper.
3.
5.
7.
4x y 5
4.
2x y 7
3x y 2
xy2
x y 1
2
3
6.
x
y 4 4
y 5x 2
x 6 3y
3x 2y 4
8.
y 2x 9
xy6
x y 3
2
2
9. The sum of two numbers is 2. Their difference is 10. Find the numbers.
10. One number is three times another number. The difference of the two numbers is
2. Find the numbers.
Determine the number of solutions for each system. Do not graph.
11. 2x y 4
12. 3x 6y 12
3x y 1
x 2y 10
13. 8x 6y 10
14. 12x 4y 1
3y 5 4x
© Glencoe/McGraw-Hill
3x y 0
187
MathMatters 3