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 substitution:
y = x - 4
y = 4x - 10
(2,-2)
Solve the system of linear equations by elimination:
x + 3y = 5
-x - y = -3
(2,1)
One solution, Infinite Solutions, No Solution
If it forms a straight line
Solve the system of linear equations by graphing:
y = x + 4
y = -x + 2
(-1,3)
Solve the system of linear equations by substitution:
y = 2x + 5
y = 3x - 1
(6,17)
Solve the system of linear equations by elimination:
x - 2y = -7
3x + 2y = 3
(-1,3)
Solve the system of linear equations:
y = 2x - 2
y = 2x + 9
No solution.
What is the standard form of a linear equation?
y=mx+b
Solve the system of linear equations by graphing:
y = 2x + 5
y = 0.5x - 1
(-4,-3)
Solve the system of linear equations by substitution:
x = 2y + 7
3x - 2y = 3
(-2, -4.5)
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.
In the equation y=-2x+5 what is the slope and what is the y-intercept?
slope=-2
y-intercept=5
Solve the system of linear equations by graphing:
x + y = 7
y = x + 3
(2,5)
Solve the system of linear equations by substitution:
2x = y - 10
x + 7 = y
(-3,4)
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 the equation in standard form:
3x - 9 = 7y
3x - 7y = 9
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 substitution:
y - x = 0
2x - 5y = 9
(-3,-3)
Solve the system of linear equations by elimination:
x + 4y = 1
3x + 5y = 10
(5,-1)
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.
Solve the equation:
5(2 - y) + y = -6
y = 4