Lesson 14

Solving Systems of Equations

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Problem 1

  1. Write equations for the lines shown.

    Graph of two intersecting lines.

  2. Describe how to find the solution to the corresponding system by looking at the graph.
     

  3. Describe how to find the solution to the corresponding system by using the equations.
     

Solution

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Problem 2

The solution to a system of equations is \((5, \text-19)\). Choose two equations that might make up the system.

A:

\(y = \text-3x - 6\)

B:

\(y = 2x - 23\)

C:

\(y = \text-7x + 16\)

D:

\(y = x -17\)

E:

\(y = \text-2x - 9\)

Solution

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Problem 3

Solve the system of equations: \(\begin{cases} y=4x-3 \\ y=\text-2x+9 \\ \end{cases}\)

Solution

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Problem 4

Solve the system of equations: \(\begin{cases} y=\frac54x-2 \\ y= \frac {\text{-}1}{4}x+19 \\ \end{cases}\)

Solution

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Problem 5

Here is an equation: \(\frac{15(x-3)}{5}= 3(2x-3)\)

  1. Solve the equation by using the distributive property first.
  2. Solve the equation without using the distributive property.
  3. Check your solution.

Solution

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(From Unit 4, Lesson 14.)