1. Solve the system by the elimination method. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
3x + y = 19 |
x + 2y = 13 |
(x, y) |
= |
2. Solve the system by graphing. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
x + y = 9 |
−x − y = −9 |
(x, y)=
3. Solve the system by the elimination method. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
x + y = 6 |
2x + 3y = 16 (x, y)= |
Q 1)
Given equations
3x + y = 19 ------ (1)
x + 2y = 13 ------ (2)
Multiplying eq (1) with 2 we get
2 x ( 3x + y = 19)
6x + 2y = 38 ------- (3)
eq (3) minus eq (2)
6x + 2y = 38 minus x + 2y = 13 we get
5x + 0 = 25
5x = 25
x = 25 / 5 = 5
Substituting x = 5 in eq (1) we get
3 (5) + y = 19
15 +y =19
y = 19 - 15
y = 4
( x , y ) = ( 5 , 4) DEPENDENT
Q 2)
Given equations
x + y = 9 ----- (1)
- x - y = - 9 --- (2)
As eq (2) and eq (1) are similar as eq (1) multiplied by -1 gives eq (2), therefore we cannot calculate the values of ( x, y) INCONSISTENT
Q 3)
Given equations are
x + y = 6 ---- (1)
2x + 3y = 16 ---- (2)
By multiplying eq (1) by 2 we get
2 x ( x + y = 6)
2x + 2y = 12 ----- (3)
eq (2) minus eq (3) we get
2x + 3y = 16 minus 2x + 2y = 12
0 + y = 4
y = 4
Substituting y=4 in eq (1) we get
x + 4 = 6
x = 6 - 4
x = 2
therefore
( x , y) = ( 2 , 4) DEPENDENT
NOTE -- eq in the above answers represents equation
1. Solve the system by the elimination method. (Enter your answers as a comma-separated list. If...
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