Both Y =
Substitution Method
Elimination Method
Review
Regents Questions
100
Solve the system of equations below by graphing or using substitution.
y = 3x - 6
y = -x + 2
(2,0)
100
y = 2x + 3
4x + 2y = -2
(-1,1)
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 by graphing or using substitution.
y = 4x - 3
y = 2x + 3
(3,9)
200
x = -2y + 1
3x + 6y = 3
Infinite Solutions
200
What is the solution of the system of equations below?
2x - 5y = 11
-2x + 3y = -9
(3, -1)
200
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
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
JC has $200 and deposits $8 each week. Kyla has $420 and withdraws $12 each week.
Write a system of equations to model this situation.
y = 8x + 200
y = -12x + 420
300
x = -4y - 2
3x + 7y = 9
(10, -3)
300
What is the solution of the system of equations below?
2x + 3y = 7
x + y = 3
(2, 1)
300
What is the solution to this system of equations?
(-1,3)
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
JC has $200 and deposits $8 each week. Kyla has $420 and withdraws $12 each week.
When will they have the same balance?
11 weeks
400
3x + 5y = 41
y = 4x - 1
(2,7)
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
Is the point (2,-1) the solution to this system of equations?
y = 3x - 7
4x - 5y = 13
Yes
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.