Problem 103 - College Algebra

Question

If \(x=3, y=2,\) and \(z=-3,\) does the ordered triple \((x, y, z)\) satisfy the equation \(2 x-y+4 z=-8 ?\)

Step-by-Step Solution

Answer

Yes, the ordered triple \( (3, 2, -3) \) satisfies the equation \( 2x - y + 4z = -8 \), because substituting these values into the equation results in an identity.

Step 1: Substitution Step

Substitute the given values into the equation. The equation becomes: \(2(3) - 2 + 4(-3)\).

Step 2: Simplification Step

Now it's necessary to perform the arithmetic operations. This leads us to \(6 - 2 - 12\)

Step 3: Final Calculation Step

Continue with the operations, which results in: \(-8\).