3 Chapter Test
Do you know HOW?
Without graphing, classify each system. Then find the solution to each system using a graph.
-
{
y
=
5
x
−
2
y
=
x
+
4
left brace . table with 2 rows and 2 columns , row1 column 1 , y equals , column 2 5 x minus 2 , row2 column 1 , y equals , column 2 x plus 4 , end table
-
{
3
x
+
2
y
=
9
3
x
+
2
y
=
4
left brace . table with 2 rows and 1 column , row1 column 1 , 3 x plus 2 y equals 9 , row2 column 1 , 3 x plus 2 y equals 4 , end table
Solve the system by substitution.
-
{
0.3
x
−
y
=
0
y
=
2
+
0.25
x
left brace . table with 2 rows and 1 column , row1 column 1 , 0.3 x minus y equals 0 , row2 column 1 , y equals 2 plus , 0.25 , x , end table
Solve the system by elimination.
-
{
4
x
−
2
y
=
3
y
−
2
x
=
−
3
2
left brace . table with 2 rows and 1 column , row1 column 1 , 4 x minus 2 y equals 3 , row2 column 1 , y minus 2 x equals negative , 3 halves , end table
-
{
3
x
+
4
y
=
9
2
x
+
y
=
6
left brace . table with 2 rows and 1 column , row1 column 1 , 3 x plus 4 y equals 9 , row2 column 1 , 2 x plus y equals 6 , end table
Graph the solution of each system.
-
{
2
x
+
y
<
3
x
<
y
+
3
left brace . table with 2 rows and 1 column , row1 column 1 , 2 x plus y less than 3 , row2 column 1 , x less than y plus 3 , end table
-
{
|
x
+
3
|
>
y
y
>
2
x
−
1
left brace . table with 2 rows and 1 column , row1 column 1 , vertical line x plus 3 vertical line greater than y , row2 column 1 , y greater than 2 x minus 1 , end table
Graph the system of constraints. Identify all vertices. Then find the values of x and y that maximize or minimize the objective function.
-
{
x
≤
5
y
≤
4
x
≥
0
y
≥
0
left brace . table with 4 rows and 1 column , row1 column 1 , x less than or equal to 5 , row2 column 1 , y less than or equal to 4 , row3 column 1 , x greater than or equal to 0 , row4 column 1 , y greater than or equal to 0 , end table
Maximum for P = 2x + y
Solve each system.
-
{
x
−
y
+
z
=
0
3
x
−
2
y
+
6
z
=
9
−
x
+
y
−
2
z
=
−
2
left brace . table with 3 rows and 4 columns , row1 column 1 , x minus , column 2 y plus , column 3 z equals , column 4 0 , row2 column 1 , 3 x minus , column 2 2 y plus , column 3 6 z equals , column 4 9 , row3 column 1 , negative x plus , column 2 y minus , column 3 2 z equals , column 4 negative 2 , end table
-
{
2
x
+
y
+
z
=
8
x
+
2
y
−
z
=
−
5
z
=
2
x
−
y
left brace . table with 3 rows and 1 column , row1 column 1 , 2 x plus y plus z equals 8 , row2 column 1 , x plus 2 y minus z equals negative 5 , row3 column 1 , z equals 2 x minus y , end table
Do you UNDERSTAND?
Write a matrix that represents the system. Then solve the system. Tell what method you used and why.
-
{
−
a
+
4
b
+
2
c
=
−
8
3
a
+
b
−
4
c
=
9
b
=
−
1
left brace . table with 3 rows and 1 column , row1 column 1 , negative eh plus 4 b plus 2 c equals negative 8 , row2 column 1 , 3 eh plus b minus 4 c equals 9 , row3 column 1 , b equals negative 1 , end table
-
Sales A pizza shop makes $1.50 on each small pizza and $2.15 on each large pizza. On a typical Friday, it sells between 70 and 90 small pizzas and between 100 and 140 large pizzas. The shop can make no more than 210 pizzas in a day. How many of each size pizza must be sold in order to maximize profit?
-
Investing Your teacher invested $5000 in three funds. After a year they had $5450. The growth fund had a return rate of 12%, the income fund had a return rate of 8%, and the money market fund had a return rate of 5%. Your teacher invested twice as much in the income fund as in the money market fund. How much money was invested in each fund?
-
Writing Describe how to identify situations in which substitution may be the best method for solving a system of equations.
-
Open-Ended Write a system of constraints whose graph is a parallelogram.
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