GeoGebra Classroom

# Zipping, Zapping, and Zooming In (1 of 2)

## OBJECTIVE: To learn how to solve simultaneous equations algebraically (substitution method)

﻿ In a previous lesson, you learned how to solve simultaneous equations using the Graphing Method. Meeting on the Dot: https://www.geogebra.org/m/dtnyh2rk In this lesson, you'll learn the first of two algebraic methods for solving simultaneous equations—the Substitution Method (Zipping). In the next lesson, you'll learn the second method—the Elimination Method (Zapping)—to Zoom In on the solution to systems of linear equations. The Substitution Method works best when both linear equations are written in SLOPE-INTERCEPT FORM (y = mx +b). Since the value of y is the same for both equations at the point of intersection, the two expressions containing x may be equated to each other and solved for x. Then the value of y may be solved using either of the two original equations.

## THANK YOU, PROFESSOR LEONARD!

Use the applet below for practice on the Substitution Method.

## INSTRUCTIONS:

1. On a separate sheet, solve the equations shown on the applet using the Substitution Method. 2. Confirm your answer by checking the box marked "Check Answer." 3. If your answer is correct, create a new problem by moving the red and blue lines. You may rotate the lines by dragging one of the dots on each line. If your answer is wrong, rework the problem and correct your mistakes before creating a new problem. Repeat as many times as needed until you master the concept.

## Applet by GeoGebra Materials Team

The applet below is another variation for solving simultaneous linear equations by substitution. If y is easy to isolate in one of the equations (as when it has no numerical coefficient), then isolate y in that equation and replace y in the other equation with the resulting expression in x. The process is demonstrated in the applet below by moving the slider marked "working." An analogous process may be applied if x is the variable that's easy to isolate.

## INSTRUCTIONS:

1. Create a problem by setting initial values for a, b, c, m, and n using the sliders. Set "working" to 0. 2. On a separate sheet, solve the equations shown on the applet using the substitution method. Follow the working demo. 3. Confirm your answer by moving the slider marked "working." 4. If your answer is correct, create a new problem by changing the values of a, b, c, m, and n using the sliders. If your answer is wrong, rework the problem and correct your mistakes before creating a new problem. Repeat as many times as needed until you master the concept.

## TODAY you learned how to solve systems of two linear equations using the Substitution Method (Zipping).

In the next lesson, you'll learn how to solve simultaneous systems using the Elimination Method (Zapping). Did you have FUN doing today's activities?