Graphing or Substitution Method
Substitution Method
Elimination Method
Review
Vocab
100
Solve the system of equations below by graphing.
y = 3x - 6
y = -x + 2
(2,0)
one solution
100
Solve the system of equations below.
y = 2x + 3
4x + 2y = -2
4x + 2(2x + 3) = -2
4x + 4x + 6 = -2, 8x + 6 = -2, 8x = -8, x =-1
y = 2(-1) + 3, y = 1
(-1,1)
one solution
100
What is the value of x in the solution of the system of equations below?
3x + 2y = 12
5x - 2y = 4
8x = 16
x = 2
100
What is the solution to this system of equations?
no solution, lines are parallel
100
The point where two lines intersect.
The solution
200
Solve the system of equations below by graphing.
y = 4x - 3
y = 2x + 3
(3,9)
one solution
200
Solve the system of equations below by substitution.
x = -2y + 1
3x + 6y = 3
NO Solution
3(-2y + 1) + 6y = -3
-6y + 3 + 6y = -3,
3 Does NOT equal -3
NO Solution
200
What is the solution of the system of equations below?
2x - 5y = 11
-2x + 3y = -9
-2y = 2
y = -1
-2x + 3(-1) = -9 , -2x = -6, x = 3
(3, -1)
200
What is the solution to this system of equations?
(-1,3)
200
The method where you can eliminate one of the variables.
The elimination method.
300
Solve the system of equations below by Graphing.
y = -2x + 2
y = -2x - 2
no solution
300
Solve the system of equations below by substitution.
x = -4y - 2
3x + 7y = 9
(10, -3)
one solution
3(-4y - 2) + 7y = -9
-12y - 6 + 7y = 9, -5y = 15, y = -3
x = -4(-3) + 2 = , 12 - 2 = 10
300
What is the solution of the system of equations below?
-4x-2y=-12
4x+8y=-24
6y = -36, y = -6
-4x - 2(-6) = -12, -4x = -24, x = 6
(6, -6)
one solution
300
If a system of equations has NO SOLUTIONS and this is one equation, what could be another equation for this system?
y = -5x - 4
Any equation in y = mx + b form with a slope of -5, but a different y-intercept.
Ex: y = -5x + 4
300
The type of solution when you graph a set of parallel lines.
No solution.
400
Solve the system of equations below by graphing.
x - y = 2
x = -2
y = x - 2
x = -2
(-2, -4)
one solution
400
Solve the system of equations below by substitution.
3x + 5y = 41
y = 4x - 1
(2,7) one solution
3x + 5(4x - 1) = 41
3x + 20x - 5 = 41, 23x = 46, x = 2
y = 4(2) - 1, y = 7
400
What is the solution of the system of equations below?
2x + 4y = 6
3x = 12 - 6y
No Solution, 0 Does NOT = -6
2x + 4y = 6
3x + 6y = 12
3[2x + 4y = 6] ... 6x + 12y = 18
-2[3x + 6y = 12]...-6x - 12y = -24 , 0 = -6, NO
400
If a system of equations has INFINITE SOLUTIONS and this is one equation, what would be the other equation for this system?
y = 2x + 4
y = 2x + 4
400
How do you express the solution for a system of equations?
An ordered pair..... (x,y)
500
Solve the system of equations below.
-4x + y = 3
x + y= -2
(-1, -1)
one solution
500
Solve the system of equations below by substitution.
y = 5x - 7
-3x - 2y = -12
(2, 3) one solution
-3(x) - 2(5x - 7) = -12
-3x -10x +14 = -12
-13x = -14-12, -13x = -26, x = 2
y = 5(2) - 7 , y = 3
500
What is the solution of the system of equations below?
2x - 6y=12
-5x+15y=-30
Infinite Solutions
5[ 2x - 6y = 12] 10x - 30y = 60
2[-5x+15y=-30] -10x + 30y = -60
0 = 0500
Is the point (2,-1) the solution to this system of equations?
y = 3x - 7
4x - 5y = 13
yes, when x = 2 & y = -1 both equations are true
y = 3x - 7.... -1 = 3(2) - 7...., -1 = -1 yes
4x - 5y = 13 .....4(2) - 5(-1) = 13, 13 = 13
500
The the best method(s) you can use if both equations are in slope-intercept form?
Graphing or Substitution