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Systems of Linear Equations
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Terms in this set (14)
System of Linear Equations
two or more linear equations that use the same variables
Is (8,9) a solution of the system of linear equations?
-8x + y = -55
x + y = -1
No
Graph each equation. Estimate the solution of the system of equations.
y − 4x= 0
y = -2x − 6
(1,4)
Graph each equation. Estimate the solution of the system of equations.
y = 3x − 10
y = 3x + 1
No Solution
Without graphing the equations, decide whether the system has one solution, no solution, or infinitely many solutions.
2y = x − 9
4x − 4y = 18
One Solution
How many solutions does this system have?
x + 4y = 0
12y = −3x
Infinitely Many Solutions
Solve the system of equations by substitution.
y = 3x − 10
3x + 2y = 16
(4,2)
River C is 400 miles longer than River D. If the sum of their lengths is 5,530 miles, what is the length of each river?
Equations:
C = 400 + D
C + D = 5530
River C = 2,965 miles
River D = 2,565 miles
Find the most efficient algebraic method to solve this system of equations. And Solve.
−3x + 4y = 9
3x − 2y = − 9
Addition Method
Answer: (-3,0)
Find the most efficient algebraic method to solve thus system of equations. And Solve.
y = 3x + 9
3x − 3y = − 9
Substitution Method
Answer: (-3,0)
Find the most efficient algebraic method to solve thus system of equations. And Solve.
4x - 3y = 7
10x - 3y = 31
Subtraction
Answer: (4,3)
Together, teammates Pedro and Ricky got 2680 base hits last season. Pedro had 280 more hits than Ricky. How many hits did each player have?
Equations:
P + R = 2680
P = 280 + R
Pedro = 1,480 hits
Ricky = 1,200 hits
Explain why the following is not a system of linear equations
8p - 6q = -17
It is only a single equation
You plant two flowers in a garden. the equations y = 11.3x +16 and y = 6.2x + 16 model the heights y of the flowers, in millimeters, after x days. What does the y-intercept of each equation represent?
The height when planted
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