For the given system of equations, considering different systems are split by ;, we have that:
- No solutions: 3y = x + 2, 9y = 3x + 7; y = 2x + 3, y = 2x + 5
- One solution: 2y = 3x, -5y = -10x,; x = 6, y = 9.
- Infinitely many solutions: y = 5x + 2, 3y = 15x + 6.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
It's equations can be written in the format:
Ax = b
Using the above format, we have that:
- If A is different from zero, the system has one solution.
- If A is zero and B is different of zero, the system has no solutions.
- If both are zero, the system has infinite solutions.
At the first system, multiplying the first equation by -3 and adding with the second, we end up with:
0y = 0x + 2
0 = -2
Which is a false statement, hence it has no solutions.
At the second system, the equations are multiples, hence it has infinite solutions.
At the third system, the coefficients are not zero and are not multiples, and it has one solution.
In the fourth system, the one solution is already given.
At the fifth system, we have that:
2x + 3 = 2x + 5
0x = 2
Hence no solutions.
To learn more about system of equations, you can take a look at https://brainly.com/question/24342899
