Question

Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system. x - 4y + z=3 y - 3z=10 3y - 8z=24 Eliminate the y -term from the third equation.

Answer 1

To eliminate the y-term from the third equation, you can use the method of elimination. Multiply the second equation by -3 and add it to the third equation, then solve for z.

Step-by-step explanation:

Step 1:

Multiply the second equation by -3 to make the coefficient of y the same as the coefficient of y in the third equation. The new equation is -3y + 9z = -30.

Step 2:

Add the second and the new equation to eliminate y. The result is -3y + 9z + (y - 3z) = -20. Simplify to get 6z = -20.

Step 3:

Solve for z by dividing both sides of the equation by 6. The final answer is z = -20/6 or -10/3.