Question

Mark is solving the following system

x+y+Z-2 (1)
3x+2y+Z-8 (2)
14x-y-77-18 (3)
Step 1. He multiplies equation (1) by 7 and adds it to equation (3)
Step 2. He multiplies equation (3) by 2 and adds it to equation (2)
Which statement explains Mark's mistake?
A) He added equation the equations in step instead of subtracting them
B) He added equation (3) instead of equation (2) in step 1
C) He did not eliminate the same variables in steps 1 and 2
D) He did not multiply equation (3) by the same number as equation (1)

Answer 1

Mark's mistake in solving the system of equations can be explained by not eliminating the same variables in steps 1 and 2.

Step-by-step explanation:

Mark's mistake in solving the system of equations x+y+Z-2 (1), 3x+2y+Z-8 (2), and 14x-y-77-18 (3) can be explained by statement C. He did not eliminate the same variables in steps 1 and 2.

In step 1, Mark multiplied equation (1) by 7 and added it to equation (3). This eliminated the x and y variables, leaving only the z variable. However, in step 2, Mark multiplied equation (3) by 2 and added it to equation (2), which did not eliminate the z variable. This inconsistency in eliminating variables in the steps led to Mark's mistake.

To solve the system of equations correctly, Mark should have eliminated the same variables in both steps. For example, if he wanted to eliminate the z variable, he should have multiplied equation (1) by a number that would cancel out the z variable when added to equation (3) and multiply equation (2) by a number that would also cancel out the z variable when added to equation (3).