Solution
A value or values we can put in place of a variable (such as x) that makes the equation true.
System of Equations
Two or more equations that use the same variables. Sometimes these equations have one solution, infinitely many solutions, or no solutions.
Y-intercept
The y-coordinate of the point where the line on the graph crosses the y-axis
Substitution
A mathematical method that lets us replace equal numbers or expressions.
One Solution
a system of equations in which the equations have different slopes and intersect at one point
No solution
a system of equations in which the equations have the same slopes , the two lines are parallel and never intersect
Infinitely many solutions
a system of equations in which the equations are the same line, so all the points on both lines are solutions to the system
Substitution
A method for solving a system of equations algebraically by replacing one variable with another
Elimination
A method for solving a system of equations algebraically by getting rid of one variable and solving for the other.
Slope-intercept form
The most common way to write a linear equation, using the format y = mx + b
Standard form
Another format for writing a linear equation, using the format Ax + By = C
Number of months
What does the x represent in this situation?
Manny's Music Rental charges a fee of $40 plus $25 per month to rent a saxophone. Sid's Saxophones charges $25 plus $30 per month to rent the same saxophone.
y = 25x + 40
y = 30x + 25
(1,5)
y = 4x+1
3x + 2y = 13
The intersection of the lines
The solution of a system of linear equations is
(2,2)
What is the solution to the system?
(4,-4)
What is the solution to the system?
(-1,-1)
What is the solution to the system?
No Solution
y = 2x + 5
y = 2x - 7
Infinite Solutions
y = -4x + 2
4x + y = 2
(5,10)
y = x + 5
3x + y = 25
(2,1)
y = 6x - 11
-2x - 3y = -7
(4,3)
2x - 3y = -1
y = x - 1
(2,3)
y = 5x - 7
-3x - 2y = -12
(13,29)
x + y = 42
y = 2x + 3
(0,0)
y = 8x
-x + 6y = 0
(6,-6)
-4x - 2y = -12
4x + 8y = -24
(10,-1)
x - y = 11
2x + y = 19
(-1,-8)
8x + y = -16
-3x + y = -5
(1,-4)
-4x - 6y = 20
-4x + 5y = -24
(-6,0)
5x + 4y = -30
3x - 9y = -18
$8
The equations 5x + 2y = 48 and
3x + 2y = 32 represents the money collected from school concert ticket sales during two class periods. If x represents the cost of ADULT tickets and y represents the cost of STUDENT tickets, what is the cost of each Adult ti
$2
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. This is represented by the equation 3x + 4y = 12.50
Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. This is rep
2
What is the value of the y coordinate of the solution to the system of equations
x + 2y = 9 and x - y = 3?
1
What is the value of the y coodinate of the solution to the system of equations
x - 2y = 1 and x + 4y = 7?