Respuesta :
Problem 1
-9x + 2y = -1 (1)
18x - 7y = 17 (2)
To eliminate x, multiply (1) by 2 to obtain
-18x + 4y = -2
18x - 7y = 17
Add the two equations.
-3y = 15
y = -5
From (2), obtain
18x = 17 + 7y = 17 + 7*(-5) = -18
x = -1
Answer: x= -1, y = -5
Problem 2.
4x + 18y = -28 (1)
2x + 9y = -14 (2)
Divide (1) by 2 to obtain the system of equations
2x + 9y = -14
2x + 9y = -14
These two equations re identical.
Therefore there are an infinite number of solutions.
Answer:
There is no unique set of solutions.
Problem 3.
20x + y = -11 (1)
-10x - 3y = -17 (2)
Multiply (2) by 2 to obtain
20x + y = -11
-20x - 6y = -34
Add the two equations to eliminate x.
-5y = -45
y = 9
From (1), obtain
20x = -11 - y = -11 - 9 = -20
x = -1
Answer: x = -1, y = 9
Problem 4
-3x + y = 7 (1)
-6x + 2y = 12 (2)
Divide (2) to obtain the system of equations
-3x + y = 7
-3x + y = 6
Because 7 ≠ 6, th set of equations is nonsensical (inconsistent).
Answer:
The set of equations is invalid, and it has no solution.
-9x + 2y = -1 (1)
18x - 7y = 17 (2)
To eliminate x, multiply (1) by 2 to obtain
-18x + 4y = -2
18x - 7y = 17
Add the two equations.
-3y = 15
y = -5
From (2), obtain
18x = 17 + 7y = 17 + 7*(-5) = -18
x = -1
Answer: x= -1, y = -5
Problem 2.
4x + 18y = -28 (1)
2x + 9y = -14 (2)
Divide (1) by 2 to obtain the system of equations
2x + 9y = -14
2x + 9y = -14
These two equations re identical.
Therefore there are an infinite number of solutions.
Answer:
There is no unique set of solutions.
Problem 3.
20x + y = -11 (1)
-10x - 3y = -17 (2)
Multiply (2) by 2 to obtain
20x + y = -11
-20x - 6y = -34
Add the two equations to eliminate x.
-5y = -45
y = 9
From (1), obtain
20x = -11 - y = -11 - 9 = -20
x = -1
Answer: x = -1, y = 9
Problem 4
-3x + y = 7 (1)
-6x + 2y = 12 (2)
Divide (2) to obtain the system of equations
-3x + y = 7
-3x + y = 6
Because 7 ≠ 6, th set of equations is nonsensical (inconsistent).
Answer:
The set of equations is invalid, and it has no solution.
