1.5: Chapter 1 Review

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PROBLEM SET: CHAPTER 1 REVIEW

Solving Linear Equations in One Variable (1.1)

Is $x=-2$ a solution to the equation $-4x - 12 = -2$?
Solve $6x − 9 = 18$
Solve $5 − 3a = 5$
Solve $\frac{2 − 5y}{6} = −8$
Solve $7 − 9y + 12 = 3y + 11 − 11y$
Solve $\frac{1}{3} x −\frac{3}{2} + \frac{5}{2} x = \frac{5}{6} x + \frac{1}{4}$
Solve $4 (4a − 1) = 5 (a − 3) + 2 (a − 2)$
Solve $3 (4 − y) − 2 (y + 7) = −5y$
Twice the sum of a number and $4$ is equal to $3$ times the sum of the number and $1$. Find the number.

Solving Linear Equations in Two Variables (1.2)

Is the point $(3, - 2)$ on the line $5x - 2y = 11$?
Find two points on the line $2x - 6 = 0$.
Find the slope of the line whose equation is $2x + 3y = 6$.
Find the slope of the line whose equation is $y = - 3x + 5$.
Graph the line $y = \dfrac{2}{3}x - 5$ by using slope-intercept form.
Graph the line $y = -2x + 3$ by using slope-intercept form.
Find both the x and y intercepts of the line $3x - 2y = 12$.
Graph the line $5x - 3y =30$ by using intercepts.
Graph the line $2x - 3y + 6 = 0$ by using intercepts.

Determining the Equation of a Line (1.3)

Find an equation of the line whose slope is 3 and y-intercept 5.
Find an equation of the line whose x-intercept is 2 and y-intercept 3.
Find an equation of the line that has slope 3 and passes through the point (2, 15).
Find an equation of the line that has slope -3/2 and passes through the point (4, 3).
Find an equation of the line that passes through the points (0, 32) and (100, 212).
Find an equation of the x-axis.

Solving Systems of Equations in Two Variables (1.4)

Determine whether the given ordered pair is a solution to the system of equations.

$\left\{\begin{array} {l} -3x-5y &= 13\\-x+4y &= 10\end{array}\right.$ and $(-6,1)$

Answer

Yes
$\left\{\begin{array} {l} 3x+7y &= 1\\ 2x+4y &= 0 \end{array}\right.$ and $(2,3)$

Solve these two systems by graphing.

$\left\{\begin{array} {l} y &= 2x-7\\ y &= -x+2 \end{array}\right.$

Answer

$(3,-1)$
$\left\{\begin{array} {l} y &= -\dfrac{1}{2}x-1\\ y &= 3x+6 \end{array}\right.$

Solve these two systems by substitution.

$\left\{\begin{array} {l} x+5y &= 5\\ 2x+3y &= 4 \end{array}\right.$

Answer

$(-1,2)$
$\left\{\begin{array} {l} x-0.2y &= 1\\ -10x+2y &= 5 \end{array}\right.$

Solve these two systems by elimination by addition.

$\left\{\begin{array} {l} x+5y &= 5\\ 2x+3y &= 4 \end{array}\right.$

Answer

$(-1,2)$
$\left\{\begin{array} {l} x-0.2y &= 1\\ -10x+2y &= 5 \end{array}\right.$
The supply curve for a product is $y = 250x - 1000$. The demand curve for the same product is $y = - 350x + 8,000$, where x is the price and y the number of items produced. Find the following.
1. At a price of $10, how many items will be in demand?
2. At what price will 4,000 items be supplied?
3. What is the equilibrium price for this product?
4. How many items will be manufactured at the equilibrium price?
The supply curve for a product is $y = 625x - 600$ and the demand curve for the same product is $y = - 125x + 8,400$, where x is the price and y the number of items produced. Find the equilibrium price and determine the number of items that will be produced at that price.
A cell phone factory has a cost of production of $C(x)=150x+10,000$ and a revenue function $R(x)=200x$. What is the break-even point?
A musician charges $C(x)=64x+20,000$, where $x$ is the total number of attendees at the concert. The venue charges $\$80$ per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?

Answer

$(1250, $100,000)$

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