Lesson 14
Solving More Systems
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?
\(y=\text-1.5x+6\)
\(y=\text-1.5x\)
\(2y=\text-3x+6\)
\(2y+3x=6\)
\(y=\text-2x+3\)
Solution
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Problem 4
The system \(x-6y=4\), \(3x-18y=4\) has no solution.
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Change one constant or coefficient to make a new system with one solution.
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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.](https://cms-im.s3.amazonaws.com/qaPUjm1sBjLj27HhQixvPd58?response-content-disposition=inline%3B%20filename%3D%228-8.3.C.PP.Image.03.7.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.C.PP.Image.03.7.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171249Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c3912e249e100718fe548c0a9ad632a012d52bb53e3b1f4628bc40ceccdc772a)
- \(y=2x+3\)
- \(y=\text-2x+3\)
- \(y=2x-3\)
- \(y=\text-2x-3\)
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?
\(\frac43\)
\(\frac34\)
\(\frac16\)
\(\frac23\)
Solution
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(From Unit 3, Lesson 10.)