Try writing and solving your own systems of liner equations, one with infinite solutions, one with no solutions, and one with one solution write a real world scenario that goes with at least one system of equations show your work
1) Infinite solutions:
Equation 1: 2x + 3y = 10
Equation 2: 4x + 6y = 20
To show that this system has infinite solutions, we can see that Equation 2 is just twice Equation 1. This means that the two equations are essentially equivalent, and any point that satisfies one equation will satisfy the other as well.
2) No solutions:
Equation 1: 3x + 2y = 5
Equation 2: 6x + 4y = 10
To show that this system has no solutions, we can see that Equation 2 is just twice Equation 1, like in the previous example. However, in this case, this means that they are actually the same line, and there is no unique point where they intersect.
3) One solution:
Equation 1: 2x + 5y = 11
Equation 2: 3x - y = 4
To solve this system for one unique solution, we can use the substitution method:
From Equation 2, we can rearrange it to solve for y:
y = 3x - 4
Now substitute this into Equation 1:
2x + 5(3x - 4) = 11
2x + 15x - 20 = 11
17x - 20 = 11
17x = 31
x = 31/17
Substitute back into Equation 2 to find y:
y = 3(31/17) - 4
y ≈ 1
So the unique solution to this system is x ≈ 1.82, y ≈ 1.