Question

Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system. {x+y-3z=3 {-2x+3y+z=2 {x-y+2z=0 Eliminate the x -term from the second equation.

Answer 1

To eliminate the x-term from the second equation in the given system, we can use the method of substitution. Substitute the value of x from the first equation into the second equation to get the new equivalent system.

Step-by-step explanation:

To eliminate the x-term from the second equation, we can use the method of substitution.

1. Start with the equation: -2x + 3y + z = 2
2. Since we want to eliminate the x-term, we can solve the first equation for x and substitute that value into the second equation.
3. From the first equation, solve for x: x = 3z - y
4. Substitute this value of x into the second equation: -2(3z - y) + 3y + z = 2
5. Simplify the equation: -6z + 2y + z = 2
6. Combine like terms: -5z + 2y = 2

The new equivalent system after eliminating the x-term from the second equation is:

{x + y - 3z = 3

{-5z + 2y = 2

{x - y + 2z = 0