Solve by ELIMINATION
Solve by GRAPHING
Solve by SUBSTITUTION
Three Variable Systems
Mystery Box
100
What variable will be eliminated?
2x-9y=2
x+9y=5
The y variable will be eliminated
100
Find the point of intersection.
(5,2)
100
Solve the systems of equations using substitution.
x = 5
x + y = 12
(5, 7)
100
What kind of lines have no solution?
Parallel lines
100
What is the slope intercept form?
y=mx+b
200
When solving by elimination, what is the first step?
Make sure that the variables are lined up. (equations are in standard form)
200
Find the point of intersection.
(2, -7)
200
Solve the systems of equations using substitution.
y = 2x
x + y = 9
(3, 6)
200
How can we determine the solution to a system of equations when graphing?
The solution is where the lines of the equations intersect.
200
What is Standard Form of an Equation?
Ax + By = C
300
What must you do to eliminate the x?
2x-3y=9
2x+7y=1
Multiply either equation by a negative 1
300
Solve by graphing. Round to the nearest tenth if necessary.
x + y = 10
xy = 21
{(3, 7), (7,3)}
300
Solve the systems of equations using substitution.
x -5y=36
2x+y=-16
(-4,-8)
300
Determine whether the given point is in the solution set to the given system.
(-1, 5, 2)
2x + y - z = 1
x - 2y + z = -9
x - y - 2z = -8
No
300
The answer to a linear system of equations is an _______
Ordered pair/Coordinate point
An x and a y!
400
2x - 3y = -2
3x - 2y = 12
(8,6)
400
Solve using a graphing calculator. Round to the nearest tenth if necessary.
y = x2
y = 2x
{(0, 0),(2,4)}
400
Solve the systems of equations using substitution.
1/2x - 2/3y = -2
4y = 3x+ 12
Infinitely many solutions - Dependent System
{(x,y) | 4y = 3x+12}
400
x + y + z = 6
x - y - z = -4
2x + y - z = 3
{(1, 3, 2)}
400
The perimeter of a rectangle is 120 ft. If the width were doubled and the length were increased by 12 ft, the perimeter would be 200.5 ft.
Width 28.25 ft
Length 31.75 ft
500
Solve using elimination method
3x - y=9
2y - 6x=7
No solution, Inconsistent System
The solution set is empty
500
Solve the system by graphing on a calculator. Round to the nearest hundredth if necessary.
y = 6x+7
y = x2
{(7, 49), (-1, 1)}
500
Solve the systems of equations using substitution.
y = 2x + 1000
0.05x + 0.06y = 400
(1/3, -5)
500
x + y - z = 0
3x - y + 3z = -2
x + 2y - 3z = -1
{(-2, 5, 3)}
500
The City Zoo has different admission prices for adults and children. When three adults and two children went to the zoo, the bill was $54.75. If two adults and three children got in for $49, then what is the price of an adult ticket and child ticket?
Adult tickets are $13.25
Child tickets are $7.50