Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Name: __________________________________
CC.A.REI.7: Solve a simple system consisting of a linear equation and a quadratic
equation in two variables algebraically and graphically. For example, find the
points of intersection between the line y=–3x and the circle x2+y2=3.
1 Let
and
. On the set of
axes below, draw the graphs of
and
.
Using this graph, determine and state all values
of x for which
.
2 On the set of axes below, solve the following
system of equations graphically and state the
coordinates of all points in the solution set.
Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Name: __________________________________
3 On the set of axes below, solve the following
system of equations graphically for all values
of x and y. State the coordinates of all
solutions.
5 Solve the following system of equations:
[The use of the grid is optional.]
4 Solve the following system of equations
algebraically or graphically for x and y:
6 Solve the following system of equations
algebraically or graphically for x and y:
Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Name: __________________________________
7 Solve the following system of equations
algebraically or graphically for x and y:
8 Solve the following systems of equations
graphically, on the set of axes below, and state
the coordinates of the point(s) in the solution
set.
9 On the set of axes below, solve the following
system of equations graphically for all values
of x and y. State the coordinates of all
solutions.
10 On the set of axes below, solve the following
system of equations graphically for all values
of x and y.
Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Name: __________________________________
11 On the set of axes below, solve the following
system of equations graphically for all values
of x and y.
12 On the set of axes below, solve the following
system of equations graphically and state the
coordinates of all points in the solution set.
13 On the set of axes below, graph the following
system of equations. Using the graph,
determine and state all solutions of the system
of equations.
14 Solve the following system of equations
graphically. State the coordinates of all points
in the solution.
Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Name: __________________________________
15 On the set of axes below, graph the following
system of equations.
16 Solve the following system of equations
graphically.
Using the graph, determine and state the
coordinates of all points in the solution set for
the system of equations.
17 On the set of axes below, solve the following
system of equations graphically for all values
of x and y.
Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Name: __________________________________
18 On the set of axes below, solve the system of
equations graphically and state the coordinates
of all points in the solution.
19 A rocket is launched from the ground and
follows a parabolic path represented by the
equation
. At the same time, a
flare is launched from a height of 10 feet and
follows a straight path represented by the
equation
. Using the accompanying
set of axes, graph the equations that represent
the paths of the rocket and the flare, and find
the coordinates of the point or points where the
paths intersect.
Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Name: __________________________________
20 A company is considering building a
manufacturing plant. They determine the
weekly production cost at site A to be
while the production cost at site B is
, where x represents the number of
products, in hundreds, and
and
are
the production costs, in hundreds of dollars.
Graph the production cost functions on the set
of axes below and label them site A and site B.
State the positive value(s) of x for which the
production costs at the two sites are equal.
Explain how you determined your answer. If
the company plans on manufacturing 200
products per week, which site should they use?
Justify your answer.
Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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1 ANS:
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Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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Regents Exam Questions CC.A.REI.7: Quadratic-Linear Systems 5
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20 ANS:
The graphs of the production costs intersect at
should use Site A, because the cost of Site A is lower at
.
REF: 061437ai
. The company