Table of Contents

- 1 What is the first step in solving a system by graphing?
- 2 How do you tell if a system is independent dependent or inconsistent?
- 3 When would you use graphing to solve a system of equations?
- 4 Why does the elimination method work when solving a system of equations?
- 5 What is an example of an inconsistent equation?
- 6 How to solve a system of linear equations graphically?
- 7 Can you graph a system to determine its solution?

## What is the first step in solving a system by graphing?

In fact, the whole graphic method process can be boiled down to three simple steps: Transform both equations into Slope-Intercept Form. Sketch the graph of each linear equation in the same coordinate plane. Determine the solution of the system.

**What is the first step in solving a system by substitution quizlet?**

Steps solve a linear system by substitution: Solve one of the equations for a variable. Substitute the equivalent expression for the variable in step 1 into the other equation. Solve the resulting equation for the other variable.

### How do you tell if a system is independent dependent or inconsistent?

If a consistent system has exactly one solution, it is independent .

- If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
- If a system has no solution, it is said to be inconsistent .

**What is the first step to solve this system of linear equation?**

- Step 1 : First, solve one linear equation for y in terms of x .
- Step 2 : Then substitute that expression for y in the other linear equation.
- Step 3 : Solve this, and you have the x -coordinate of the intersection.
- Step 4 : Then plug in x to either equation to find the corresponding y -coordinate.

#### When would you use graphing to solve a system of equations?

Graphing: Graphing is the best method to use when introducing a new student to solving systems of two equations in two variables, because it gives them a visiual to recognize what they are looking for. Graphing is less exact and often takes more time than the other methods.

**How do you write system of linear equations?**

Writing Systems of Linear Equations from Word Problems

- Understand the problem. Understand all the words used in stating the problem. Understand what you are asked to find.
- Translate the problem to an equation. Assign a variable (or variables) to represent the unknown.
- Carry out the plan and solve the problem.

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

The Elimination Method. 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. And since x + y = 8, you are adding the same value to each side of the first equation.

**What is the result of adding the system of equations 2x y 4 3x y 6?**

The result of adding the system of equations 2x + y = 4, 3x – y = 6 is 5x = 10.

### What is an example of an inconsistent equation?

Inconsistent equations is defined as two or more equations that are impossible to solve based on using one set of values for the variables. An example of a set of inconsistent equations is x+2=4 and x+2=6.

**How do you tell if a system of equations has no solution?**

A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

#### How to solve a system of linear equations graphically?

To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.

**How do you solve a system of equations?**

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.

## Can you graph a system to determine its solution?

Yes, in both cases we can still graph the system to determine the type of system and solution. If the two lines are parallel, the system has no solution and is inconsistent. If the two lines are identical, the system has infinite solutions and is a dependent system. Precalculus.

**How are the equations of a graphing system dependent?**

o If the lines are the same (the graphs intersect at all points), the system is a consistent system of linear equations and the equations are dependent. That is, any solution of one equation must also be a solution of the other, so the equations depend on each other. The following terms refer to whether the system has any solutions at all.