Remember how the solutions to a system of equations are found graphically and analyze the structure of the equations forming the system.
Number of Solutions: No solution. Explanation: No point lies in all three planes. The three planes are parallel.
Practice makes perfect
Let's start by reviewing how we can solve a system of equations by graphing. When graphing a system of three equations with three variables, each equation represents a plane in a coordinate space. The intersections of these planes are the solution to our system. Let's have a look to our system.
We can see that the left-hand sides of Equation (I) and Equation (II) are the same, while the right-hand side is different. This will be represented graphically as two parallel planes. Furthermore, notice that left-hand side of Equation (III) is a multiple of the left-hand side of the first two equations. Let's divide Equation (III) by -2.
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