System of Equations and Inequalities
er
1 AmrBoard vs CollegeBoard 3 AmrBoard vs CollegeBoard
4𝑥 − 2𝑦 > 8 𝑥 = 2𝑦 − 5
lp
Which of the following ordered pairs (x. y) are in the 𝑦 = −2𝑥 + 5
solution set for the inequality above?
I. (-1,-10)
The ordered pair (x. y) satisfies the system of equations
II. (2,0)
He
above. What is the value of x + y
III. (1,-2)
A) -5
A) I only B) 0
5
B) II only C)
2
H
C) III only D) 4
D) I and II only
AT
TM
2 AmrBoard vs CollegeBoard
4 AmrBoard vs CollegeBoard
𝑦 = 𝑥2 + 𝑥 − 2 𝑦 − 7𝑥 = 13
𝑥+𝑦 =1
SA
8𝑥 = 3𝑦
If (x . y) is a solution of the system of equations above, Which ordered pair ( x , y ) is the solution to the system
which of the following is a possible value of XY? of equations above?
A) 7
B) 1 A) ( -8, -3 )
rd
C) -1
B) ( -3, -8 )
D) -12 3
C) ( 1, 8 )
oa
8
D) ( 3
,1)
rB
AmrBoard SAT Helper - System of Equations and Inequalities 1
Am
, 5 AmrBoard vs CollegeBoard 7 AmrBoard vs CollegeBoard
3𝑥 = 𝑦 At a coffee shop, Don combined Arabica beans with
3𝑥 = 36 − 𝑦 Robusta beans to make a coffee bean blend. The
er
Based on the system of equations above, what is the Arabica beans cost $13.50 per pound, and the
value of y?
Robusta beans cost $9.25 per pound. He used 1.2
A) 9
lp
pounds of Robusta beans in the blend, and the
B) 12
total cost of the blend was $21.90. how many
C) 15
pounds of Arabica beans did dun use in the blend?
D) 18
He
H
6 AmrBoard vs CollegeBoard
3𝑥 + 7𝑦 = 14
AT
𝑎𝑥 + 28𝑦 = 56 8 AmrBoard vs CollegeBoard
TM
In the system of the equation above, a is a
X + 2y = 16
constant. If the system has infinitely many 0.5x – y = 10
solutions, what is the value of a? The solution to the system of equations above is ( x , y ).
SA
what is the value of x?
A) 2 A) -2
B) 2
B) 3
C) 18
C) 4
rd
D) 36
D) 12
oa
rB
AmrBoard SAT Helper - System of Equations and Inequalities 2
Am
, 9 AmrBoard vs CollegeBoard 11 AmrBoard vs CollegeBoard
𝑥2 − 6𝑥 + 11 = 𝑦 At a snack bar, each medium drink costs $1.85 and each
large drink costs c more dollars than a medium drink. If 5
X=y+1 medium drinks and 5 large drinks cost a total of U20.50,
er
what is the value of c?
The system of equations above is graphed in the
A) 0.45
Xy-plane. Which of the following is the y-coordinate of
an intersection point ( x , y ) of the graphs of two B) 0.40
lp
equation ?
C) 0.30
A) -4
D) 0.25
B) -2
He
C) 2
D) 4
H
AT12 AmrBoard vs CollegeBoard
10 AmrBoard vs CollegeBoard If 𝑥 4 − 𝑦 4 = −15 𝑎𝑛𝑑 𝑥2 − 𝑦 2 = −3, what is the
value of 𝑥2 + 𝑦 2 ?
TM
Students in a science lab are working in groups to build A) 5
both a small and a large electrical circuit. A large circuit B) 4
C) 2
SA
uses 4 resistors and 2 capacitors, and a small circuit uses D) 1
3 resistors and 1 capacitor. There are 100 resistors and
70 capacitors available, and each group must have
enough resistors and capacitors to make one large and
one small circuit. What is the maximum number of
rd
groups that could work on this lab project?
oa
rB
AmrBoard SAT Helper - System of Equations and Inequalities 3
Am
er
1 AmrBoard vs CollegeBoard 3 AmrBoard vs CollegeBoard
4𝑥 − 2𝑦 > 8 𝑥 = 2𝑦 − 5
lp
Which of the following ordered pairs (x. y) are in the 𝑦 = −2𝑥 + 5
solution set for the inequality above?
I. (-1,-10)
The ordered pair (x. y) satisfies the system of equations
II. (2,0)
He
above. What is the value of x + y
III. (1,-2)
A) -5
A) I only B) 0
5
B) II only C)
2
H
C) III only D) 4
D) I and II only
AT
TM
2 AmrBoard vs CollegeBoard
4 AmrBoard vs CollegeBoard
𝑦 = 𝑥2 + 𝑥 − 2 𝑦 − 7𝑥 = 13
𝑥+𝑦 =1
SA
8𝑥 = 3𝑦
If (x . y) is a solution of the system of equations above, Which ordered pair ( x , y ) is the solution to the system
which of the following is a possible value of XY? of equations above?
A) 7
B) 1 A) ( -8, -3 )
rd
C) -1
B) ( -3, -8 )
D) -12 3
C) ( 1, 8 )
oa
8
D) ( 3
,1)
rB
AmrBoard SAT Helper - System of Equations and Inequalities 1
Am
, 5 AmrBoard vs CollegeBoard 7 AmrBoard vs CollegeBoard
3𝑥 = 𝑦 At a coffee shop, Don combined Arabica beans with
3𝑥 = 36 − 𝑦 Robusta beans to make a coffee bean blend. The
er
Based on the system of equations above, what is the Arabica beans cost $13.50 per pound, and the
value of y?
Robusta beans cost $9.25 per pound. He used 1.2
A) 9
lp
pounds of Robusta beans in the blend, and the
B) 12
total cost of the blend was $21.90. how many
C) 15
pounds of Arabica beans did dun use in the blend?
D) 18
He
H
6 AmrBoard vs CollegeBoard
3𝑥 + 7𝑦 = 14
AT
𝑎𝑥 + 28𝑦 = 56 8 AmrBoard vs CollegeBoard
TM
In the system of the equation above, a is a
X + 2y = 16
constant. If the system has infinitely many 0.5x – y = 10
solutions, what is the value of a? The solution to the system of equations above is ( x , y ).
SA
what is the value of x?
A) 2 A) -2
B) 2
B) 3
C) 18
C) 4
rd
D) 36
D) 12
oa
rB
AmrBoard SAT Helper - System of Equations and Inequalities 2
Am
, 9 AmrBoard vs CollegeBoard 11 AmrBoard vs CollegeBoard
𝑥2 − 6𝑥 + 11 = 𝑦 At a snack bar, each medium drink costs $1.85 and each
large drink costs c more dollars than a medium drink. If 5
X=y+1 medium drinks and 5 large drinks cost a total of U20.50,
er
what is the value of c?
The system of equations above is graphed in the
A) 0.45
Xy-plane. Which of the following is the y-coordinate of
an intersection point ( x , y ) of the graphs of two B) 0.40
lp
equation ?
C) 0.30
A) -4
D) 0.25
B) -2
He
C) 2
D) 4
H
AT12 AmrBoard vs CollegeBoard
10 AmrBoard vs CollegeBoard If 𝑥 4 − 𝑦 4 = −15 𝑎𝑛𝑑 𝑥2 − 𝑦 2 = −3, what is the
value of 𝑥2 + 𝑦 2 ?
TM
Students in a science lab are working in groups to build A) 5
both a small and a large electrical circuit. A large circuit B) 4
C) 2
SA
uses 4 resistors and 2 capacitors, and a small circuit uses D) 1
3 resistors and 1 capacitor. There are 100 resistors and
70 capacitors available, and each group must have
enough resistors and capacitors to make one large and
one small circuit. What is the maximum number of
rd
groups that could work on this lab project?
oa
rB
AmrBoard SAT Helper - System of Equations and Inequalities 3
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