Chapter 7

Solve the equation. $$ 3 x+7=-2 $$

use the following information. You can run 200 meters per minute uphill and 250 meters per minute downhill. One day you run a total of 2200 meters in 10 minutes. Assign labels to the verbal model below. Then write an algebraic model.

Use the following information. You are planning the menu for your restaurant. For Saturday night you plan to serve roast beef and teriyaki chicken. You expect to serve at least 240 pounds of meat that evening and that less beef will be ordered than chicken. The roast beef costs 5 dollars per pound and the chicken costs 3 dollars per pound. You have a budget of at most 1200 dollars for meat for Saturday night. Graph the system of linear inequalities.

In Exercises 32 and 33, use the following information. The graph below represents the need for low-income rental housing in the United States and the number of affordable rental units available. Use the points (0, 6200) and (25, 10,500) to write an equation for the number of housing units needed. Then use the points (0, 6500) and (25, 6100) to write an equation for the number of affordable units available.

Use the following information. A carpenter is buying supplies for the next job. The job requires 4 sheets of oak paneling and 2 sheets of shower tileboard. The carpenter pays \(99.62\) for these supplies. For the following job the carpenter buys 12 sheets of oak paneling and 6 sheets of shower tileboard and pays \( 298.86\) Can you find how much the carpenter is spending on 1 sheet of oak paneling? Explain.

Use linear combinations to solve the linear system. Then check your solution. \(-3 p+2=q\) \(-q+2 p=3\)

Solve the equation. $$ 15-2 a=7 $$

use the following information. You can run 200 meters per minute uphill and 250 meters per minute downhill. One day you run a total of 2200 meters in 10 minutes. Find the number of meters you ran uphill and the number of meters you ran downhill.

Use the following information. A carpenter is buying supplies for the next job. The job requires 4 sheets of oak paneling and 2 sheets of shower tileboard. The carpenter pays \( 99.62\) for these supplies. For the following job the carpenter buys 12 sheets of oak paneling and 6 sheets of shower tileboard and pays \(298.86\) If the carpenter later spends a total of \(\$ 139.69\) for 8 sheets of oak paneling and 1 sheet of shower tileboard, can you find how much 1 sheet of oak paneling costs? Explain.

Use linear combinations to solve the linear system. Then check your solution. \(t+r=1\) \(2 r-t=2\)

Solve the equation. $$ 2 y+3 y=5 $$

Use the following information. You have 10,000 dollars to buy spotlights for your theater. A medium-throw spotlight costs 1000 dollars and a long-throw spotlight costs 3500 dollars . The current play needs at least 3 medium-throw spotlights and at least 1 long-throw spotlight. Write a system of linear inequalities for the number \(m\) of medium-throw spotlights and the number \(l\) of long-throw spotlights that models both your budget and the needs of the current play.

You plant a 14-inch spruce tree that grows 4 inches per year and an 8-inch hemlock tree that grows 6 inches per year. After how many years will the trees be the same height? How tall will each be?

Use the following system. $$6 x-9 y=n \quad \text { Equation } 1$$ $$-2 x+3 y=3 \quad \text { Equation } 2$$ Find a value of n so that the linear system has infinitely many solutions.

Use linear combinations to solve the linear system. Then check your solution. \(3 g-24=-4 h\) \(-2+2 h=g\)

Solve the equation. $$ 21=7(w-2) $$

Which linear system has the solution (6, 6)? a. \(4 x-3 y=-1\) \(-2 x+y=-3\) b. \(x+y=12\) \(3 x-2 y=6\) c. \(3 x+y=4\) \(4 x-3 y=1\) d. \(4 x+3 y=0\) \(2 x-y=0\)

Use the following system. $$6 x-9 y=n \quad \text { Equation } 1$$ $$-2 x+3 y=3 \quad \text { Equation } 2$$ Find a value of n so that the linear system has no solution.

Use linear combinations to solve the linear system. Then check your solution. \(x+1=3 y\) \(2 x=7-3 y\)

Solve the equation. $$ -2(t-5)=26 $$

Which linear system has been correctly solved for one of the variables from the following system? $$ \begin{aligned} &2 x-y=-1\\\ &2 x+y=-7 \end{aligned} $$ $$ f. \quad \begin{aligned} &2 x-y=-1\\\ &y=2 x-7 \end{aligned} $$ $$ g.\quad \begin{aligned} &2 x-y=-1\\\ &y=-2 x+7 \end{aligned} $$ $$ h. \quad \begin{aligned} &y=2 x+1\\\ &2 x+y=-7 \end{aligned} $$ $$ j. \quad \begin{aligned} &y=-2 x-1\\\ &2 x+y=-7 \end{aligned} $$

Use linear combinations to solve the linear system. Then check your solution. \(4 a=-b\) \(a-b=5\)

Solve the equation. $$ 4(2 x+3)=-4 $$

Your math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test? a). 5 points: 54 2 points: 46 b). 5 points: 46 2 points: 54 c). 5 points: 30 2 points: 8 d). 5 points: 8 2 points: 30

Use the following information. You can work a total of no more than 20 hours per week at your two jobs. Baby-sitting pays 5 dollars per hour, and your job as a cashier pays 6 dollars per hour. You need to earn at least 90 dollars per week to cover your expenses. Write a system of inequalities that shows the various numbers of hours you can work at each job.

You and your friend go to a Mexican restaurant. You order 2 tacos and 2 enchiladas and your friend orders 3 tacos and 1 enchilada. Your bill was 4.80 dollar and your friend’s bill was 4.00 dollar. Which system of linear equations represents the situation? $$(A) 2 t+2 e=4.00 3 t+e=4.80$$ $$(B) 2 t+2 e=4.00 t+3 e=4.80$$ $$(C) 2 t+2 e=4.80 3 t+e=4.00$$ $$(D) 2 t+2 e=4.80 t+3 e=4.00$$

Use linear combinations to solve the linear system. Then check your solution. \(\begin{aligned} 2 m-4 &=4 n \\ m-2 &=n \end{aligned}\)

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope. $$ (3,0), m=-4 $$

Simplify the expression. $$ 4 g+3+2 g-3 $$

Use the following information. You can work a total of no more than 20 hours per week at your two jobs. Baby-sitting pays 5 dollars per hour, and your job as a cashier pays 6 dollars per hour. You need to earn at least 90 dollars per week to cover your expenses. Graph the system of linear inequalities.

Use the following information. You are climbing a 300 foot cliff. By 1: 00 P.M. you have climbed 110 feet up the cliff. By 3: 00 P.M. you have reached a height of 220 feet. Find the slope of the line that passes through the points \((1,110)\) and \((3,220)\) What does it represent?

Use linear combinations to solve the linear system. Then check your solution. \(3 y=-5 x+15\) \(-y=-3 x+9\)

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope. $$ (-4,3), m=1 $$

Determine whether the graphs of the two equations are parallel lines. Explain. $$line a: y=4 x+3\quad line b: 2 y-8 x=-3$$

Simplify the expression. $$ 3 x+2-(5 x+2) $$

Use the following information. You can work a total of no more than 20 hours per week at your two jobs. Baby-sitting pays 5 dollars per hour, and your job as a cashier pays 6 dollars per hour. You need to earn at least 90 dollars per week to cover your expenses. Give two possible ways you could divide your hours between the two jobs.

Use the following information. You are climbing a 300 foot cliff. By 1: 00 P.M. you have climbed 110 feet up the cliff. By 3: 00 P.M. you have reached a height of 220 feet. If you continue climbing the cliff at the same rate, at what time will you reach the top of the cliff?

Use linear combinations to solve the linear system. Then check your solution. \(3 j+5 k=19\) \(j-2 k=-1\)

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope. $$ (1,-5), m=4 $$

Determine whether the graphs of the two equations are parallel lines. Explain. $$line a: 4 y+5 x=1\quad line b. 10 x+2 y=2$$

Simplify the expression. $$ 6(2-m)-3 m-12 $$

Graph the inequality. $$x<2$$

Use linear combinations to solve the linear system. Then check your solution. \(6 x+2 y=5\) \(8 x+2 y=3\)

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope. $$ (-4,-1), m=-2 $$

Determine whether the graphs of the two equations are parallel lines. Explain. $$ \begin{aligned} &\text { line a: } 3 x+9 y+2=0\\\ &\text { line } b: 2 y=-6 x+3 \end{aligned} $$

Simplify the expression. $$ 4(3 a+5)+3(-4 a+2) $$

Graph the inequality. $$y \geq 5$$

Use linear combinations to solve the linear system. Then check your solution. \(3 x+7 y=6\) \(2 x+9 y=4\)

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope. $$ (2,3), m=2 $$

Determine whether the graphs of the two equations are parallel lines. Explain. $$line a: 4 y-1=5\quad line b: 6 y+2=8$$