IM Alg1.2.13 Lesson: Solving Systems by Substitution

Here are graphs of two equations in a system.

Select the systems which could be represented by the graphs. Be prepared to explain how you know.

[math]\begin{cases} 3x = 8\\3x + y = 15 \end{cases}[/math] [math]\begin{cases} y = \text-7x + 13 \\y = \text-1 \end{cases}[/math] [math]\begin{cases} y = 2x - 7\\4 + y = 12 \end{cases}[/math] [math]\begin{cases} x + 2y = 8 \\x = \text-5 \end{cases}[/math]

Here are four systems of equations you saw earlier. Solve each system. Then, check your solutions by substituting them into the original equations to see if the equations are true.

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]

[math]\begin{cases} y = 2x - 7\\4 + y = 12 \end{cases}[/math][br]

Solve each system without graphing.

[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} 2d = 8f \\ 18 - 4f = 2d \end{cases}[/math][br]

[math]\begin{cases} w + \frac17z = 4 \\ z = 3w –2 \end{cases}[/math][br]

Solve this system with four equations.

[math]\begin{cases}3 x + 2y - z + 5w= 20 \\ y = 2z-3w\\ z=w+1 \\ 2w=8 \end{cases}[/math]

IM Alg1.2.13 Lesson: Solving Systems by Substitution

Here are graphs of two equations in a system.

Here are four systems of equations you saw earlier. Solve each system. Then, check your solutions by substituting them into the original equations to see if the equations are true.

Solve each system without graphing.

Solve this system with four equations.

Information: IM Alg1.2.13 Lesson: Solving Systems by Substitution