Practice and Problem-Solving Exercises
A Practice
See Problems 1 and 2.
Solve each system by elimination. Check your answers.
-
{
x
−
y
+
z
=
−
1
x
+
y
+
3
z
=
−
3
2
x
−
y
+
2
z
=
0
left brace . table with 3 rows and 1 column , row1 column 1 , x minus y plus z equals negative 1 , row2 column 1 , x plus y plus 3 z equals negative 3 , row3 column 1 , 2 x minus y plus 2 z equals 0 , end table
-
{
x
−
y
−
2
z
=
4
−
x
+
2
y
+
z
=
1
−
x
+
y
−
3
z
=
11
left brace . table with 3 rows and 1 column , row1 column 1 , x minus y minus 2 z equals 4 , row2 column 1 , negative x plus 2 y plus z equals 1 , row3 column 1 , negative x plus y minus 3 z equals 11 , end table
-
{
−
2
x
+
y
−
z
=
2
−
x
−
3
y
+
z
=
−
10
3
x
+
6
z
=
−
24
left brace . table with 3 rows and 1 column , row1 column 1 , negative 2 x plus y minus z equals 2 , row2 column 1 , negative x minus 3 y plus z equals negative 10 , row3 column 1 , 3 x plus 6 z equals negative 24 , end table
-
{
a
+
b
+
c
=
−
3
3
b
−
c
=
4
2
a
−
b
−
2
c
=
−
5
left brace . table with 3 rows and 4 columns , row1 column 1 , eh plus , column 2 b plus , column 3 c equals , column 4 negative 3 , row2 column 1 , , column 2 3 b minus , column 3 c equals , column 4 4 , row3 column 1 , 2 eh minus , column 2 b minus , column 3 2 c equals , column 4 negative 5 , end table
-
{
6
q
−
r
+
2
s
=
8
2
q
+
3
r
−
s
=
−
9
4
q
+
2
r
+
5
s
=
1
left brace . table with 3 rows and 4 columns , row1 column 1 , 6 q minus , column 2 r plus , column 3 2 s equals , column 4 8 , row2 column 1 , 2 q plus , column 2 3 r minus , column 3 s equals , column 4 negative 9 , row3 column 1 , 4 q plus , column 2 2 r plus , column 3 5 s equals , column 4 1 , end table
-
{
x
−
y
+
2
z
=
−
7
y
+
z
=
1
x
=
2
y
+
3
z
left brace . table with 3 rows and 1 column , row1 column 1 , x minus y plus 2 z equals negative 7 , row2 column 1 , y plus z equals 1 , row3 column 1 , x equals 2 y plus 3 z , end table
-
{
3
x
+
3
y
+
6
z
=
9
2
x
+
y
+
3
z
=
7
x
+
2
y
−
z
=
−
10
left brace . table with 3 rows and 4 columns , row1 column 1 , 3 x plus , column 2 3 y plus , column 3 6 z equals , column 4 9 , row2 column 1 , 2 x plus , column 2 y plus , column 3 3 z equals , column 4 7 , row3 column 1 , x plus , column 2 2 y minus , column 3 z equals , column 4 negative 10 , end table
-
{
3
x
−
y
+
z
=
3
x
+
y
+
2
z
=
4
x
+
2
y
+
z
=
4
left brace . table with 3 rows and 4 columns , row1 column 1 , 3 x minus , column 2 y plus , column 3 z equals , column 4 3 , row2 column 1 , x plus , column 2 y plus , column 3 2 z equals , column 4 4 , row3 column 1 , x plus , column 2 2 y plus , column 3 z equals , column 4 4 , end table
-
{
x
−
2
y
+
3
z
=
12
2
x
−
y
−
2
z
=
5
2
x
+
2
y
−
z
=
4
left brace . table with 3 rows and 4 columns , row1 column 1 , x minus , column 2 2 y plus , column 3 3 z equals , column 4 12 , row2 column 1 , 2 x minus , column 2 y minus , column 3 2 z equals , column 4 5 , row3 column 1 , 2 x plus , column 2 2 y minus , column 3 z equals , column 4 4 , end table
-
{
x
+
2
y
=
2
2
x
+
3
y
−
z
=
−
9
4
x
+
2
y
+
5
z
=
1
left brace . table with 3 rows and 4 columns , row1 column 1 , x plus , column 2 2 y , column 3 equals , column 4 2 , row2 column 1 , 2 x plus , column 2 3 y minus , column 3 z equals , column 4 negative 9 , row3 column 1 , 4 x plus , column 2 2 y plus , column 3 5 z equals , column 4 1 , end table
-
{
3
x
+
2
y
+
2
z
=
−
2
2
x
+
y
−
z
=
−
2
x
−
3
y
+
z
=
0
left brace . table with 3 rows and 4 columns , row1 column 1 , 3 x plus , column 2 2 y plus , column 3 2 z equals , column 4 negative 2 , row2 column 1 , 2 x plus , column 2 y minus , column 3 z equals , column 4 negative 2 , row3 column 1 , x minus , column 2 3 y plus , column 3 z equals , column 4 0 , end table
-
{
x
+
4
y
−
5
z
=
−
7
3
x
+
2
y
+
3
z
=
7
2
x
+
y
+
5
z
=
8
left brace . table with 3 rows and 4 columns , row1 column 1 , x plus , column 2 4 y minus , column 3 5 z equals , column 4 negative 7 , row2 column 1 , 3 x plus , column 2 2 y plus , column 3 3 z equals , column 4 7 , row3 column 1 , 2 x plus , column 2 y plus , column 3 5 z equals , column 4 8 , end table
