Graphing
Substitution Method
Elimination Method
Review
Regents Questions
100
Solve the system of equations below.
y = 3x - 6
y = -x + 2
(2,0)
one solution
100
Solve the system of equations below.
y = 2x + 3
4x + 2y = -2
(-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
x = 2
100
What is the solution to this system of equations?
no solution
100
Using the substitution method, Vito is solving the following system of equations algebraically:
y + 3x = −4
2x − 3y = −21
Which equivalent equation could Vito use?
1) 2(−3x − 4) + 3x = −21
2) 2(3x − 4) + 3x = −21
3) 2x − 3(−3x − 4) = −21
4) 2x − 3(3x − 4) = −21
#3
200
Solve the system of equations below.
y = 4x - 3
y = 2x + 3
(3,9)
one solution
200
Solve the system of equations below.
x = -2y + 1
3x + 6y = 3
Infinitely many solutions
200
What is the solution of the system of equations below?
2x - 5y = 11
-2x + 3y = -9
(3, -1)
200
What is the solution to this system of equations?
(-1,3)
200
What is the solution to the system of equations below?
y = 2x + 8
3(−2x + y) = 12
1) no solution
2) infinite solutions
3) (−1,6)
4) (1/2, 9)
#1
300
Solve the system of equations below.
y = -2x + 2
y = -2x - 2
no solution
300
Solve the system of equations below.
x = -4y - 2
3x + 7y = 9
(10, -3)
one solution
300
What is the solution of the system of equations below?
2x + 3y = 7
x + y = 3
(2, 1)
300
If a system of equations has NO SOLUTIONS and this is one equation, what would be the other equation?
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
When solved graphically, which system of equations will have exactly one point of intersection?
1) y = -x - 20 and y = x + 17
2) y = 0.5x + 30 and y = 0.5x - 30
3) y = 3/5x + 12 and y = 0.6x - 19
4) y = -x + 15 and y = -x + 25
#1
400
Solve the system of equations below.
x - y = 2
x = -2
(-2, -4)
one solution
400
Solve the system of equations below.
3x + 5y = 41
y = 4x - 1
(2,7)
one solution
400
What is the solution to the system of equations below? y = 2x + 8
3(−2x + y) = 12
24 does not equal 12
no solution
400
If a system of equations has INFINITE SOLUTIONS and this is one equation, what would be the other equation?
y = 2x + 4
y = 2x + 4
400
In attempting to solve the system of equations
y = 3x − 2 and 6x − 2y = 4, John graphed the two equations on his graphing calculator. Because he saw only one line, John wrote that the answer to the system is the empty set. Is he correct? Explain your answer.
No. There are infinite solutions.
500
Solve the system of equations below.
-2x - y = 1
-6x = 3y + 3
infinitely many solutions
500
Solve the system of equations below.
y = 5x - 7
-3x - 2y = -12
(2, 3)
one solution
500
What is the solution to the system of equations below?
-5x + y = -3
3x - 8y = 24
(0, -3)
500
Is the point (2,-1) the solution to this system of equations?
y = 3x - 7
4x - 5y = 13
yes
500
#3 is (4,2)