Answer:
First equation: no solution
Second equation: one solution
Third equation: one solution
Fourth equation: one solution
Fifth equation: one solution
Step-by-step explanation:
First system: 3x - 2y = 3; 6x - 4y = 1
Multiplying the first equation by two, we have:
6x - 4y = 6
As this equation and the second equation of the system have the same coefficients to x and y, but a different independent value (1 and 6), the system has no solution
Second system: 3x - 5y = 8; 5x - 3y = 2
From the first equation: x = (8 + 5y)/3
Using this value of x in the second equation, we have:
(40 + 25y)/3 - 3y = 2
40 + 25y - 9y = 6
16y = 34
y = 2.125
x = (8 + 5*2.125)/3 = 6.2083
The system has one solution
Third system: 3x + 2y = 8; 4x + 3y = 1
From the first equation: x = (8 - 2y)/3
Using this value of x in the second equation, we have:
(32 - 8y)/3 +3y = 1
32 - 8y + 9y = 3
y = -29
x = (8 - 2*(-29))/3 = 22
The system has one solution
Fourth system: 3x - y = 3; 2x - 4y = 2
From the first equation: y = 3x - 3
Using this value of y in the second equation, we have:
2x - 12x + 12 = 2
10x = 10
x = 1
y = 3 - 3 = 0
The system has one solution
Fifth system: 3x - 4y = 2; 6x - y = 1
From the first equation: 3x = 2 + 4y
Using this value of 3x in the second equation, we have:
4 + 8y - y = 1
7y = -3
y = -0.4286
x = (2 + 4y) / 3 = (2 + 4*(-0.4286)) / 3 = 0.0952
The system has one solution
