Table of Contents

## How do you find a system of equations algebraically?

The Elimination Method: Both equations are in standard form: Ax + By = C. The system of equations are solved by eliminating a variable and solving for the remaining variable. Add the two equations together to eliminate the y, then solve for x.

**What are the 2 ways to solve a system of equations algebraically?**

There are two methods that will be used in this lesson to solve a system of linear equations algebraically. They are 1) substitution, and 2) elimination. They are both aimed at eliminating one variable so that normal algebraic means can be used to solve for the other variable.

### What does solving algebraically mean?

Solving an algebraic equation just means manipulating the equation so that the variable is by itself on one side of the equation and everything else is on the other side of the equation. Once everything else is simplified, the equation is solved.

**How do you solve an equation algebraically and graphically?**

To solve an equation means to find all the values that make the statement true. To solve an equation graphically, draw the graph for each side, member, of the equation and see where the curves cross, are equal. The x values of these points, are the solutions to the equation.

## What does it mean if algebraically you found a solution that does not appear on the graph?

If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.

**What does it mean to prove something algebraically?**

An algebraic proof shows the logical arguments behind an algebraic solution. You are given a problem to solve, and sometimes its solution. If you are given the problem and its solution, then your job is to prove that the solution is right.

### What are the three methods for solving system of equations?

The three methods most commonly used to solve systems of equation are substitution, elimination and augmented matrices. Substitution and elimination are simple methods that can effectively solve most systems of two equations in a few straightforward steps.

**How do you solve each system by graphing?**

Solve systems of equations by graphing. A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system.

## How to solve basic algebra problems?

Define a variable.

**How do you solve the system using substitution?**

Solving Systems by Substitution. The method of solving “by substitution” works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, “substituting” for the chosen variable and solving for the other.