## How do you solve a matrix using inverses?

Create the inverse of the coefficient matrix out of the matrix equation. Multiply the inverse of the coefficient matrix in the front on both sides of the equation. Cancel the matrix on the left and multiply the matrices on the right. Multiply the scalar to solve the system.

Table of Contents

### How do you solve the system using the elimination method?

To Solve a System of Equations by Elimination

- Write both equations in standard form.
- Make the coefficients of one variable opposites.
- Add the equations resulting from Step 2 to eliminate one variable.
- Solve for the remaining variable.
- Substitute the solution from Step 4 into one of the original equations.

#### What are the 4 steps for solving systems of equations by elimination?

Step 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. Step 3: Add or subtract the equations. Step 4: Substitute back in to find the other variable.

**How do you find the inverse of a system?**

Finding the Inverse of a Function

- First, replace f(x) with y .
- Replace every x with a y and replace every y with an x .
- Solve the equation from Step 2 for y .
- Replace y with f−1(x) f − 1 ( x ) .
- Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.

**Why does the elimination method work when solving a system of equations?**

The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.

## What is the first step in solving a system of equations by elimination?

Step 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. Step 3: Add or subtract the equations. Step 4: Plug back in to find the other variable.

### How do I find the inverse of a 3×3 matrix?

To find the inverse of a 3×3 matrix, first calculate the determinant of the matrix. If the determinant is 0, the matrix has no inverse. Next, transpose the matrix by rewriting the first row as the first column, the middle row as the middle column, and the third row as the third column.