Page 453 - Algebra 1

Example
3
Classifying Systems of Equations
Determine if each system of equations is consistent and independent, consistent and dependent, or inconsistent.
a. x-_1y=_3 44
2x + y = 1 SOLUTION
Solve the system of equations.
Math Reasoning
Write Why is there only one solution for a system of independent and consistent equations?
x - _1 y = _3 44
2x + y = 1
Use substitution.
y = 4x - 3
y = -2x + 1 -2x + 1 = 4x - 3
_2 = x 3
y = 4 x - 3
y = -2x + 1
Substitute y = -2x + 1 in the first equation. Solve for x.
Substitute _2 for x in one of the original equations and solve for y. 3
_2
2(3 )+ y = 1
y = -_1 3
_2
Substitute 3 for x in the second equation.
_2
The solution is (3 , - 3 ). There is exactly
one solution, so the system is consistent and independent.
Check Graphthelinesandverifythesolution. b. 3x+y=2
_1
Solve for y.
y = -2x
y = 4x - 3
x
O
-1
1
y = -3x - 4
SOLUTION Write the equations in slope-intercept form.
3x + y = 2 y = -3x + 2 y = -3x - 4
-1
The two equations have the same slope and different y-intercepts. The lines are parallel, so there is no solution. The system is inconsistent.
Check Graphthelinesandverifythesolution.
y =
y
8
-3x - 4
x
-8
-4
4
8
-4
438 Saxon Algebra 1
+ 1 1
y
y
= -3x + 2
-8