Understanding Systems of Equations

Front

What are the three types of solutions to a system of equations?

Back

1. 1. One Solution

2. 2. No Solution

3. 3. Infinite Solutions

Front

What determines the solution of a system of equation when graphing?

Back

Where the lines intersect.

solution: (x , y)

Front

What is the solution of a system when the equations are the exact same?

Back

Infinite Solutions

(Same Line)

Front

What is the solution of a system of equations where the slope of both equations are equal BUT not the y-intercept?

Back

No Solutions.

(Parallel Lines)

Front

Steps to Solving by Graphing.

Back

1. 1. Both equations need to be in Slope-Intercept. (y = mx + b)

2. 2. Plot into Desmos.

3. 3. Locate where the lines intersect.

4. 4. Answer the question; they want x, y, or both?

Front

Solve by Elimination method steps.

Back

1. 1. Eliminate x or y variable.

2. 2. Solve for x or y.

3. 3. Plug value back in.

4. 4. Solve for second variable.

Front

Substitution Method steps.

Back

1. 1. Substitute the x or y variable from one equation into the other.

2. 2. Solve for x or y.

3. 3. Plug value back in.

4. 4. Solve for second variable.

Front

Steps to convert from Standard to Slope Intercept.

Back

1. 1. Move the term with x variables.

2. 2. Divide by coefficient of y.

Front

How to graph y = mx +b?

Back

1. 1. Locate Slope(m) and Y-Intercept(b).

2. 2. Plot b on y-axis.

3. 3. Plot second point using m.

4. 4. Connect the dots.

Front

What is the solution to the system of equation.

Back

(5, 1)