5.03 Graphing systems of equations
State whether the following graphs show a system of equations with:
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No solutions
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One solution
Infinitely many solutions
State the solution to the following systems of equations in the form \left(x, y\right).
Consider the following linear equations:
Equation 1: y = 4x - 3
Equation 2: y = 4 - 3x
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| y |
Fill in the table of values using the line y = 4x - 3.
Fill in the table of values using the line y = 4 - 3x.
State the slope of the line y = 4x - 3.
State the slope of the line y = 4 - 3x.
Sketch the graph of both lines on the same coordinate axes.
Consider the following linear equations:
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y = \dfrac{x}{3} + \dfrac{1}{3}
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- 8 y = 8 x + 8
Determine the intercepts of the line y = \dfrac{x}{3} + \dfrac{1}{3}.
Determine the intercepts of the line - 8 y = 8 x + 8.
Sketch the graph of both lines on the same coordinate axes.
State the values of x and y which satisfy both equations.
Consider the following linear equations:
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y = 2 x + 2
y = - 2 x + 2
Determine the slope and y-intercept of the line y = 2 x + 2.
Determine the intercepts of the line y = - 2 x + 2.
Sketch the graph of both lines on the same coordinate axes.
State the values of x and y which satisfy both equations.
Consider the following systems of linear equations:
Sketch the graph of both lines on the same coordinate axes.
State if there exists a value for x and y that satisfy the two equations simultaneously. If yes, state the values of x and y.
y = - 4 x - 1
y = - 4 x + 2
4 x - 2 y = 2
- 2 x + 4 y = 2
y = 5 x - 7
y = - x + 5
y = x + 0
y = - 1
A system of linear equations has no solutions. One of the equations of the system is \\ y = - 4 x - 3. Which equation could be the other equation of the system?
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y = - 4 x - 4
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y = - \dfrac{x}{4} - 3
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y = 4 x + 3
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y = \dfrac{x}{4} - 4
Consider the graph of the equation \\ y = 5 x + 3:
If a second line y = mx + b intersects this line at the point \left(0, 3\right), which of the following statements is true?
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b = 3
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m > 5
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m = 5
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m < 0
Consider the system of linear equations:
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Equation 1: y = x - 2
Equation 2: y = 5 x - 6
Add equations 1 and 2 to create equation 3. State equation 3.
Sketch the graph of equations 1, 2 and 3 on the same coordinate axes.
Determine the solution to the system of equations.
Consider the system of linear equations:
Equation 1: 2 x + y = - 2
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Equation 2: 2 x + 5 y = 14
Multiply Equation 1 by 3 and add it to Equation 2 to create Equation 3. State Equation 3.
Sketch the graph of equations 1, 2 and 3 on the same coordinate axes.
Determine the solution to the system of equations.
A rectangular zone is to be 4 \text{ ft} longer than it is wide, with a total perimeter of 32 \text{ ft}.
Let y represent the length of the rectangle and x represent the width.
Write the two equations that represent the information.
Sketch the graph of the two equations on the same axes.
Hence, find the values of the length and width of the rectangle.
Write a scenario to represent the system of equations and its solution. Explain what the solution to the system means in terms of the scenario.
Two equations, y_1 and y_2 represent the growth of two different house plants over time. Use the graph of y_1 and y_2 to support the claim that the two plants will never reach the same height on the same day.
Describe a situation where it would be unfeasible to solve a system of equations by graphing.