Solving Systems of Linear Equations by Graphing
Solve the system of linear equations by graphing:
y = 2x + 9
y = -x + 6
(-1,7)
Solve the system of linear equations by elimination:
x + 3y = 5
-x - y = -3
(2,1)
Solve the system of linear equations:
y = 2x - 2
y = 2x + 9
No solution.
Solve the equation:
5(2 - y) + y = -6
y = 4
Solve the system of linear equations by graphing:
y = x + 4
y = -x + 2
(-1,3)
Solve the system of linear equations by elimination:
x - 2y = -7
3x + 2y = 3
(-1,3)
Solve the system of linear equations:
y = 3x + 1
-x + 2y = -3
(-1,-2)
Write the equation in standard form:
3x - 9 = 7y
3x - 7y = 9
Solve the system of linear equations by graphing:
y = 2x + 5
y = 0.5x - 1
(-4,-3)
Solve the system of linear equations by elimination:
2x + 7y = 1
2x - 4y = 12
(4,-1)
Solve the system of linear equations:
y = 5x - 9
y = 5x + 9
No solution.
Decide whether the two equations are equivalent and solve if possible.
4n + 1 = n - 8
3n = -9
Yes; n = -3
Solve the system of linear equations by graphing:
x + y = 7
y = x + 3
(2,5)
Solve the system of linear equations by elimination:
2x - y = 0
3x - 2y = -3
(3,6)
Solve the system of linear equations:
y = 8x - 2
y - 8x = -2
Infinitely many solutions.
Write an equation of the line that passes through the given points:
(0,0) and (2,6)
y = 3x
Is it possible for a system of linear equations to have exactly two solutions? Explain your reasoning.
No, two lines cannot intersect in exactly two points.
Solve the system of linear equations by elimination:
x + 4y = 1
3x + 5y = 10
(5,-1)
Describe and correct the error in solving the system of linear equations.
y = -2x + 4
y = -2x + 6
The lines have the same slope so there are infinitely many solutions.
The lines have the same slope but different y-intercepts so therefore they are never going to intersect = No Solution.
When solving a system of linear equations algebraically, how do you know when the system has no solution?
When solving a system of linear equations algebraically, how do you know when the system has infinitely many solutions?
When solving a system of linear equations algebraically, you know the system has no solution when you reach an invalid statement such as -3 = 2.
Infinitely many solutions has a valid statement such as 1 = 1.