Problem 3 - College Algebra Essentials

Question

Determine if the given ordered triple is a solution of the system. $$\begin{aligned} &(4,1,2)\\\ &\left\\{\begin{aligned} x-2 y &=2 \\ 2 x+3 y &=11 \\ y-4 z &=-7 \end{aligned}\right. \end{aligned}$$

Step-by-Step Solution

Answer

Yes, the ordered triple (4,1,2) is a solution to the given system of equations.

Step 1: Substitute into the first equation

Substitute x = 4, y = 1 into the first equation. This gives:\n\( 4 - 2(1) = 2 \) which simplifies to 2 = 2.

Step 2: Substitute into the second equation

Next, substitute x = 4, y = 1 into the second equation. This provides:\n\( 2(4) + 3(1) = 11 \) which simplifies to 11 = 11.

Step 3: Substitute into the third equation

Lastly, substitute y = 1, z = 2 into the third equation. This gives:\n\( 1 - 4(2) = -7 \) which simplifies to -7 = -7.

Step 4: Interpret the results

Since substituting the ordered pair (4,1,2) into all three equations yielded true statements (2=2, 11=11 and -7=-7), this means the ordered triple (4,1,2) is indeed a solution of the system.