Lesson 14

Solving More Systems

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Problem 1

Solve: \(\begin{cases} y=6x \\ 4x+y=7 \\ \end{cases}\)

Solution

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Problem 2

Solve: \(\begin{cases} y=3x \\ x=\text-2y+70 \\ \end{cases}\)

Solution

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Problem 3

Which equation, together with \(y=\text-1.5x+3\), makes a system with one solution?

A:

\(y=\text-1.5x+6\)

B:

\(y=\text-1.5x\)

C:

\(2y=\text-3x+6\)

D:

\(2y+3x=6\)

E:

\(y=\text-2x+3\)

Solution

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Problem 4

The system \(x-6y=4\), \(3x-18y=4\) has no solution.

  1. Change one constant or coefficient to make a new system with one solution.

  2. Change one constant or coefficient to make a new system with an infinite number of solutions.

Solution

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Problem 5

Match each graph to its equation.

Four graphs, each with a line in the x y plane. 
  1. \(y=2x+3\)
  2. \(y=\text-2x+3\)
  3. \(y=2x-3\)
  4. \(y=\text-2x-3\)

Solution

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(From Unit 3, Lesson 11.)

Problem 6

Here are two points: \((\text-3,4)\), \((1,7)\). What is the slope of the line between them?

A:

\(\frac43\)

B:

\(\frac34\)

C:

\(\frac16\)

D:

\(\frac23\)

Solution

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(From Unit 3, Lesson 10.)