How many solutions does the system of equations below have? 3x - y - 3z = 9 -x + y + 2z = -11 -2x + 2y + z = -10 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Question

How many solutions does the system of equations below have? 3x - y - 3z = 9 -x + y + 2z = -11 -2x + 2y + z = -10     Choices: (A)no solution (B)one solution (C)infinitely many solutions

Bytelearn · Accepted Answer

Write Equations: First, let's write down the system of equations to see what we're working with: 3x - y - 3z = 9 -x + y + 2z = -11 -2x + 2y + z = -10Check Coefficients: We can use the method of elimination or substitution to solve the system, but before that, let's check if the coefficients of the variables are multiples of each other, which might indicate no solution or infinitely many solutions.Eliminate Variables: Looking at the coefficients of x, y, and z in each equation, they don't seem to be simple multiples of each other, so we can't immediately conclude that there are no solutions or infinitely many solutions.Add Equations: Let's try to eliminate one variable by adding or subtracting the equations. If we add the first and second equations, we can eliminate y: (3x - y - 3z) + (-x + y + 2z) = 9 - 11 2x - z = -2Simplify Second Equation: Now, let's add the second and third equations to eliminate y again: (-x + y + 2z) + (-2x + 2y + z) = -11 - 10 -3x + 3z = -21Identify Mistake: We can simplify the second equation we got by dividing by -3: -3x + 3z = -21 x - z = 7 Oops, we made a mistake here. We should have divided all terms by 3, not just the x term.

How many solutions does the system of equations below have? $\newline$ $3x - y - 3z = 9$ $\newline$ $-x + y + 2z = -11$ $\newline$ $-2x + 2y + z = -10$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

Full solution

More problems from Determine the number of solutions to a system of equations in three variables

Related topics