Problem 4 - College Algebra Essentials

Question

Determine if the given ordered triple is a solution of the system. $$\begin{aligned} &(-1,3,2)\\\ &\left\\{\begin{aligned} x-2 z &=-5 \\ y-3 z &=-3 \\ 2 x-z &=-4 \end{aligned}\right. \end{aligned}$$

Step-by-Step Solution

Answer

The ordered triple (-1,3,2) is a solution to the system of equations.

Step 1: Check the first equation

Substitute x=-1 and z=2 into the first equation \(x-2z=-5\). This results in \((-1)-2*2=-5\) which simplifies to \(-1-4=-5\). Both sides of the equation equal -5, which means the ordered triple satisfies the first equation.

Step 2: Check the second equation

Next, substitute y=3 and z=2 into the second equation \(y-3z=-3\). This yields \(3-3*2=-3\), which simplifies to \(3-6=-3\). The left hand side equals -3, which means the ordered triple satisfies the second equation as well.

Step 3: Check the third equation

Finally, substitute x=-1 and z=2 into the third equation \(2x-z=-4\). This gives us \(2*(-1)-2=-4\), which simplifies to \(-2-2=-4\). Thus, both sides of the equation equal -4, and therefore the ordered triple also satisfies the third equation.