[br]In a previous lesson, you learned how to solve simultaneous equations using the [color=#0000ff]Graphing Method[/color].[br][br][i][color=#0000ff]Meeting on the Dot:[/color][/i] https://www.geogebra.org/m/dtnyh2rk[br][br]In this lesson, you'll learn the first of two algebraic methods for solving simultaneous equations—the [color=#0000ff]Substitution Method[/color] [color=#0000ff](Zipping).[/color] In the next lesson, you'll learn the second method—the [color=#0000ff]Elimination Method (Zapping)[/color]—to [color=#0000ff]Zoom In[/color] on the solution to systems of linear equations.[br][br]The [color=#0000ff]Substitution Method[/color] works best when both linear equations are written in [i][color=#0000ff]SLOPE-INTERCEPT FORM (y = mx +b)[/color][/i]. Since the value of [color=#0000ff]y[/color] is the same for both equations at the point of intersection, the two expressions containing [color=#0000ff]x[/color] may be equated to each other and solved for [color=#0000ff]x[/color]. Then the value of [color=#0000ff]y[/color] may be solved using either of the two original equations.

[br]Use the applet below for practice on the [color=#0000ff]Substitution Method[/color].

1. On a separate sheet, solve the equations shown on the applet using the [color=#0000ff]Substitution Method[/color].[br][br]2. Confirm your answer by checking the box marked [color=#0000ff]"Check Answer."[/color][br][br]3. If your answer is correct, create a new problem by moving the [color=#ff0000]red[/color] and [color=#0000ff]blue[/color] 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.[br][br]Repeat as many times as needed until you master the concept.

The applet below is another variation for solving simultaneous linear equations by substitution.[br][br]If [color=#0000ff]y[/color] is easy to isolate in one of the equations (as when it has no numerical coefficient), then isolate [color=#0000ff]y[/color] in that equation and replace [color=#0000ff]y[/color] in the other equation with the resulting expression in [color=#0000ff]x[/color]. The process is demonstrated in the applet below by moving the slider marked [color=#0000ff]"working." [br][br][/color]An analogous process may be applied if [color=#0000ff]x[/color] is the variable that's easy to isolate.

1. Create a problem by setting initial values for [color=#0000ff]a, b, c, m,[/color] and [color=#0000ff]n[/color] using the sliders. Set [color=#0000ff]"working"[/color] to [color=#ff0000]0[/color].[br][br]2. On a separate sheet, solve the equations shown on the applet using the substitution method. Follow the working demo.[br][br]3. Confirm your answer by moving the slider marked [color=#0000ff]"working."[/color][br][br]4. If your answer is correct, create a new problem by changing the values of [color=#0000ff]a, b, c, m,[/color] and [color=#0000ff]n[/color] using the sliders. If your answer is wrong, rework the problem and correct your mistakes before creating a new problem.[br][br]Repeat as many times as needed until you master the concept.

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