©Korhan Poroy, Sinan Akçay Equations, Equation systems – Number of solutions
1.
4.
2.
5.
6.
3. 2𝑥 + 3𝑦 = 7
−𝑚𝑥 = 𝑛𝑦 − 14
If the system of equations has infinitely many
solutions, what is the value of 𝑚 + 𝑛 ?
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©Korhan Poroy, Sinan Akçay Equations, Equation systems – Number of solutions
7.
10) 2(𝑎𝑥 + 3) − 8 = 6 − 4𝑥
For which of the following values of a, the
equation has no solution?
A) 𝑎 = 11
B) 𝑎 = −11
How many solutions exist to the given
system?
C) 𝑎 = 2
D) 𝑎 = −2
8)
9) 4(𝑥 − 2) + 𝑥 = 𝑎𝑥 − 8
If the equation has exactly one solution,
which of the following could be the value of
a?
I.3
II.5
A.NONE
B.I
C.II
D.I and II
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©Korhan Poroy, Sinan Akçay Equations, Equation systems – Number of solutions
11)
12)
3
©Korhan Poroy, Sinan Akçay Equations, Equation systems – Number of solutions
13.
𝟐𝒂𝒙 + 𝟑𝒃𝒚 = 𝟒𝒄
𝒂
𝒃
𝒄
𝒙+ 𝒚=
𝟐
𝟑
𝟒
17.
If a, b and c are constants, how many
solutions exist to the system of equations?
A) None
B) 1
C) 2
D) infinite
14. The equation
2𝑎𝑥 − 3 = 6𝑥 − 𝑏
has infinite number of solutions. What is the
value of a+b ?
15.
16. (math subject level 2 only)
98. If the equation system below
𝑎𝑥 + 𝑏𝑦 = 2
𝑐𝑥 + 𝑑𝑦 = 3
has no solution, then what
a
c
b
=?
d
  (B) -1
(C) 0
is the value of
(A) -2
(D) 1
(E) 2
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©Korhan Poroy, Sinan Akçay Equations, Equation systems – Number of solutions
18.
19)
20)
5
©Korhan Poroy, Sinan Akçay Equations, Equation systems – Number of solutions
Answers
1) A
2) A
3) 10
4) B
5) B
6) E
7) 2
8) A
9) B
10) D
11) D
12) A
13) B
14) 6
15) 5
16) C
17) C
18) B
19) A
20) C
Equation systems, number of solutions (Page 5 in the SAT booklet)
Given the system of equations
𝑎𝑥 + 𝑏𝑦 = 𝑐
𝑑𝑥 + 𝑒𝑦 = 𝑓
There is no solution (the lines are parallel) if
𝑎
𝑑
𝑏
𝑐
𝑒
𝑓
= ≠
There are infinitely many solutions (the lines are coincident) if
There is only one solution if
𝑎
𝑑
≠
𝑏
𝑒
𝑎
𝑑
𝑏
𝑐
𝑒
𝑓
= =
(The lines are intersecting)
6