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Chapter 5: Problem 81

Write a system of equations having \(\\{(-2,7)\\}\) as a solution set. (More than one system is possible.)

Short Answer

Expert verified
One possible system of equations having (-2,7) as a solution set is \(y = 3x + 13\) and \(y = -2x + 3\).

Step by step solution

01

Choose Slopes for the Equations

Choose the slope for two linear equations. Let's select 3 for the first equation and -2 for the second equation.
02

Use Slope-Intercept Form for First Equation

Substitute the coordinates (-2,7) and slope into the slope-intercept form \(y = mx + b\), where m is the slope and b is the y-intercept. The equation becomes 7 = 3(-2) + b, which after solving for b, gives b = 13.
03

Write Down the First Equation

Substitute m = 3 and b = 13 into the slope-intercept form to get the first equation as \(y = 3x + 13\)
04

Use Slope-Intercept Form for Second Equation

Substitute the coordinates (-2,7) and slope into the slope-intercept form again, but this time with slope -2. The equation becomes 7 = -2(-2) + b, which after solving for b, gives b = 3.
05

Write Down the Second Equation

Substitute m = -2 and b = 3 into the slope-intercept form to get the second equation as \(y = -2x + 3\)
06

Pair Equations Together to Form System

The system of equations that has (-2,7) as a solution is then given as: \[\[\begin{align*} y &= 3x + 13 \\ y &= -2x + 3 \end{align*}\]\]

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Most popular questions from this chapter

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(4 x=3 y+8\) \(2 x=-14+5 y\)

In Exercises \(19-30,\) solve each system by the addition method. \(2 x-7 y=2\) \(3 x+y=-20\)

In Exercises \(19-30,\) solve each system by the addition method. \(x+y=1\) \(x-y=3\)

Explain how to find the partial fraction decomposition of a rational expression with a repeated linear factor in the denominator.

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(9 x-3 y=12\) \(y=3 x-4\)
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