Page 370 - Algebra 1

All solutions of a linear equation can be found on its graph. Graphing each equation can solve a system of linear equations. If the system has one solution, the solution is the common point or the point of intersection.
Solving by Graphing
Solve the system by graphing. Then check your solution. y=x+3
y = 2x + 1
SOLUTION Graph both equations on the same coordinate plane. Find the
Example
2
point of intersection.
Check thattheorderedpair(2,5)makesboth equations true.
y = x + 3 y = 2x + 1 5 2 + 3 5 2(2) + 1 5=5 ✓ 5 4+1
y x
5=5 ✓
The ordered pair (2, 5) is a solution of each equation.
(2, 5) is a solution of the system.
-2
2
4
Example
3
Writing Equations in Slope-Intercept Form
Solve the system by graphing. Then check your solution. 3x + y = 9
x + 2y = 8
SOLUTION Write the equations in slope-intercept form.
3x + y = 9
-_ 3 _ x -_ 3 _ x
y = -3x + 9
x + 2y = 8 -x -x
Graph both equations on the same coordinate plane. Identify the point of intersection.
Check thattheorderedpair(2,3)makesboth original equations true.
+ 4
_ _ _ _ _ _
2y = -x + 8
y = - _1 x + 4 2
y
_ _1 1 x x
4
y =
(2
, 3)
3x + y = 9 3(2) + 3 9 6+3 9
9=9 ✓
x + 2y = 8 2 + 2(3) 8 2+6 8
8=8 ✓
y = -3x
2
y
6
(2, 5)
4
=
2
O
x
-4
-2
2
4
-2
The ordered pair (2, 3) is a solution of each equation. (2, 3) is a solution of the system.
Lesson 55 355
x
+ 3
2
+ 9 -4
O
y
=
2x
+
1