Lesson 7: Solving Systems by Substitution (Alg1.2.13)

[color=#0000ff][b][size=200][icon]/images/ggb/toolbar/mode_zoom.png[/icon]Math Talk[/size][/b][/color]
Here are graphs of two equations in a system.
[img]data:image/png;base64,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[/img][br][br]Select the systems which could be represented by the graphs. Be prepared to explain how you know. 
[color=#0000ff][b][size=200][icon]/images/ggb/toolbar/mode_zoom.png[/icon]Four Systems[/size][/b][/color]
Here are four systems of equations you saw earlier. Solve each system.
[size=150]Then, check your solutions by substituting them into the original equations to see if the equations are true.[/size][br]A. [br][math]\begin{cases} x + 2y = 8 \\x = \text-5 \end{cases}[/math]
B. [br][math]\begin{cases} y = \text-7x + 13 \\y = \text-1 \end{cases}[/math][br]
C. [br][math]\begin{cases} 3x = 8\\3x + y = 15 \end{cases}[/math][br]
D.[br][math]\begin{cases} y = 2x - 7\\4 + y = 12 \end{cases}[/math][br]
[color=#0000ff][b][size=200][icon]/images/ggb/toolbar/mode_pen.png[/icon]Need more practice?[/size][/b][/color]
Solve the following the systems of equations by substitution.
[math]\begin{cases} 5x – 2y = 26 \\ y + 4 = x \end{cases}[/math]
[math]\begin{cases} 2m – 2p = \text-6\\ p = 2m + 10 \end{cases}[/math][br]
[math]\begin{cases} w + \frac17z = 4 \\ z = 3w –2 \end{cases}[/math][br]
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Information: Lesson 7: Solving Systems by Substitution (Alg1.2.13)