Math Problem Statement

3x+2y-z=11, x+3y+z=16, 2x-2y+z=9

Solution

Let's solve this system of three equations using either substitution or elimination.

The given system of equations is:

  1. 3x+2yz=113x + 2y - z = 11
  2. x+3y+z=16x + 3y + z = 16
  3. 2x2y+z=92x - 2y + z = 9

Step 1: Add Equation 2 and Equation 3 to eliminate zz.

Adding these two equations cancels out zz:

(x+3y+z)+(2x2y+z)=16+9(x + 3y + z) + (2x - 2y + z) = 16 + 9 x+2x+3y2y+z+z=25x + 2x + 3y - 2y + z + z = 25 3x+y+2z=253x + y + 2z = 25

Step 2: Solve for one variable

You can solve the system using any preferred method!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Elimination Method
Substitution Method

Formulas

Equation of a straight line
Elimination Method
Substitution Method

Theorems

Linear Systems Theorem
Additive Property of Equality

Suitable Grade Level

Grades 8-10