Answer:
3x + 4y = 12; 2x – 3y = 6
Multiplying the first equation by 2 and the second equation by 3, we get:
6x + 8y = 24
6x - 9y = 18
Subtracting the second equation from the first, we get:
17y = 6
y = 6/17
Substituting y in the first equation, we get:
3x + 4(6/17) = 12
3x = 180/17 - 24/17
3x = 156/17
x = 52/17
Therefore, the solution of the given system is x = 52/17 and y = 6/17.
x + y = 3; x – y = 5
Adding the two equations, we get:
2x = 8
x = 4
Substituting x in the first equation, we get:
4 + y = 3
y = -1
Therefore, the solution of the given system is x = 4 and y = -1.
3x + 2y – z = 4; 2x – y + 3z = 4; x + y + 2z = 4
Adding the first and second equations, we get:
5x + y + 2z = 8
Subtracting the third equation from the above equation, we get:
4x + z = 4
Substituting z = 4 - 4x in the third equation, we get:
3x + 2y - (4 - 4x) = 4
7x + 2y = 8
Substituting y = (8 - 7x)/2 in the first equation, we get:
9x - z = 8
Substituting z = 4 - 4x, we get:
x = 4/5, y = 2/5, and z = 4/5
Therefore, the solution of the given system is x = 4/5, y = 2/5, and z = 4/5.
x – y + 5z = -4; 4x – 2y + 3z = 1; 3x – 2y + 6z = 6
Multiplying the first equation by -4 and adding it to the second equation, we get:
16x - 6z = 17
Multiplying the first equation by -3 and adding it to the third equation, we get:
9x + 4z = 18
Multiplying the second equation by 2 and subtracting it from the third equation, we get:
x + 6z = 8
Substituting z = (8 - x)/6 in the above equation, we get:
x = 10/3, y = 8/3, and z = 2/3
Therefore, the solution of the given system is x = 10/3, y = 8/3, and z = 2/3.
x2 + y2 = 13; 2x – 3y = -5
Squaring the second equation and simplifying, we get:
4x2 - 12xy + 9y2 = 25
Adding the above equation to the first equation, we get:
5x2 + 10y2 = 38
Sub
Explanation: