Systems of Linear Equations by Inspection

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Jane is practicing solving systems of equations by inspection. She thinks that y = 5/6x + 2 and y = 5/6x – 2 would have exactly one solution. Is she correct? Why or why not?

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If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

How many solutions will this system have?

• One

• Two

• No Solution

• Infinitely Many Solutions

The system will have (a)   solutions.

• One

• Two

• No Solution

• Infinitely Many Solutions

Answer explanation

The system has one solution because the equations are consistent and intersect at a single point. This indicates a unique solution, confirming that the correct answer is 'One'.

What is the solution to the system?

• (3, -1)

• (2, -6)

• No Solution 

• (6, -2)

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Two linear equations with the same set of variables

• system of equations

• function

• association

• correlation

Which point satisfies the system of equations shown in the table?

• (-2, -5)

• (0, -5)

• (6, 7)

• (7, 7)