Write a system of equations, three equations/three unknowns, that has (1, 2, 3) as the
solution.
so I can use whatever I want? no calculations or anything?
To write a system of equations with (1, 2, 3) as the solution, we need to define three equations with three unknowns. Let's assume the unknowns as x, y, and z.
The system of equations can be:
Equation 1: x + 2y + 3z = 1
Equation 2: 2x - y + z = 2
Equation 3: 3x + y + 2z = 3
To check if the solution (1, 2, 3) satisfies these equations, substitute the values of x, y, and z into the equations:
Equation 1: 1 + 2(2) + 3(3) = 1 + 4 + 9 = 14 (LHS)
So, Equation 1 is satisfied since 14 = 14 (RHS).
Equation 2: 2(1) - 2 + 3 = 2 - 2 + 3 = 3 (LHS)
So, Equation 2 is satisfied since 3 = 3 (RHS).
Equation 3: 3(1) + 2 + 2(3) = 3 + 2 + 6 = 11 (LHS)
So, Equation 3 is satisfied since 11 = 11 (RHS).
Hence, (1, 2, 3) is the solution to the system of equations.
just plug in the values for your equations. For example,
7x-4y+2z = 5
and so on, using whatever coefficients you want.