Chapter 5

The sum of two numbers is -26. One number is 12 less than the other. Find the numbers.

The perimeter of a rectangle is 50 . The length is 5 more than the width. Find the length and width.

The perimeter of a rectangle is 60 . The length is 10 more than the width. Find the length and width.

The perimeter of a rectangle is 58 . The length is 5 more than three times the width. Find the length and width.

The perimeter of a rectangle is \(84 .\) The length is 10 more than three times the width. Find the length and width.

The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle. Find the measure of both angles.

Maxim has been offered positions by two car dealers. The first company pays a salary of \(\$ 10,000\) plus a commission of \(\$ 1,000\) for each car sold. The second pays a salary of \(\$ 20,000\) plus a commission of \(\$ 500\) for each car sold. How many cars would need to be sold to make the total pay the same?

Jackie has been offered positions by two cable companies. The first company pays a salary of \(\$ 14,000\) plus a commission of \(\$ 100\) for each cable package sold. The second pays a salary of \(\$ 20,000\) plus a commission of \(\$ 25\) for each cable package sold. How many cable packages would need to be sold to make the total pay the same?

Amara currently sells televisions for company \(A\) at \(a\) salary of \(\$ 17,000\) plus a \(\$ 100\) commission for each television she sells. Company B offers her a position with a salary of \(\$ 29,000\) plus a \(\$ 20\) commission for each television she sells. How televisions would Amara need to sell for the options to be equal?

Mitchell currently sells stoves for company \(A\) at a salary of \(\$ 12,000\) plus a \(\$ 150\) commission for each stove he sells. Company B offers him a position with a salary of \(\$ 24,000\) plus a \(\$ 50\) commission for each stove he sells. How many stoves would Mitchell need to sell for the options to be equal?

When Gloria spent 15 minutes on the elliptical trainer and then did circuit training for 30 minutes, her fitness app says she burned 435 calories. When she spent 30 minutes on the elliptical trainer and 40 minutes circuit training she burned 690 calories. Solve the system \(\left\\{\begin{array}{l}15 e+30 c=435 \\ 30 e+40 c=690\end{array}\right.\) for \(e,\) the number of calories she burns for each minute on the elliptical trainer, and \(c,\) the number of calories she burns for each minute of circuit training.

Stephanie left Riverside, California, driving her motorhome north on Interstate 15 towards Salt Lake City at a speed of 56 miles per hour. Half an hour later, Tina left Riverside in her car on the same route as Stephanie, driving 70 miles per hour. Solve the system \(\left\\{\begin{array}{l}56 s=70 t \\\ s=t+\frac{1}{2}\end{array}\right.\) (a) for \(t\) to find out how long it will take Tina to catch up to Stephanie. (b) what is the value of \(s,\) the number of hours Stephanie will have driven before Tina catches up to her?

Solve the system of equations \(\left\\{\begin{array}{l}x+y=10 \\\ x-y=6\end{array}\right.\) (a) by graphing. (b) by substitution. (c) Which method do you prefer? Why?

Solve the system of equations \(\left\\{\begin{array}{l}3 x+y=12 \\\ x=y-8\end{array}\right.\) by substitution and explain all your steps in words.

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 5 x+2 y=2 \\ -3 x-y=0 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} -3 x+y=-9 \\ x-2 y=-12 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 6 x-5 y=-1 \\ 2 x+y=13 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x-y=-7 \\ 4 x+2 y=-6 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x+y=-1 \\ x-y=-5 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x+y=-8 \\ x-y=-6 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x-2 y=1 \\ -x+2 y=9 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} -7 x+6 y=-10 \\ x-6 y=22 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x+2 y=-3 \\ -x-2 y=-19 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 5 x+2 y=1 \\ -5 x-4 y=-7 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 6 x+4 y=-4 \\ -6 x-5 y=8 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x-4 y=-11 \\ x-2 y=-5 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 5 x-7 y=29 \\ x+3 y=-3 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 6 x-5 y=-75 \\ -x-2 y=-13 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} -x+4 y=8 \\ 3 x+5 y=10 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x-5 y=7 \\ 3 x-y=17 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 5 x-3 y=-1 \\ 2 x-y=2 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 7 x+y=-4 \\ 13 x+3 y=4 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} -3 x+5 y=-13 \\ 2 x+y=-26 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x-5 y=-9 \\ 5 x+2 y=16 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 4 x-3 y=3 \\ 2 x+5 y=-31 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 4 x+7 y=14 \\ -2 x+3 y=32 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 5 x+2 y=21 \\ 7 x-4 y=9 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x+8 y=-3 \\ 2 x+5 y=-3 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 11 x+9 y=-5 \\ 7 x+5 y=-1 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x+8 y=67 \\ 5 x+3 y=60 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x+9 y=-4 \\ 3 x+13 y=-7 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} \frac{1}{3} x-y=-3 \\ x+\frac{5}{2} y=2 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x+\frac{1}{2} y=\frac{3}{2} \\ \frac{1}{5} x-\frac{1}{5} y=3 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x+\frac{1}{3} y=-1 \\ \frac{1}{2} x-\frac{1}{3} y=-2 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x+y=3 \\ 6 x+3 y=9 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x-4 y=-1 \\ -3 x+12 y=3 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} -3 x-y=8 \\ 6 x+2 y=-16 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 4 x+3 y=2 \\ 20 x+15 y=10 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x+2 y=6 \\ -6 x-4 y=-12 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 5 x-8 y=12 \\ 10 x-16 y=20 \end{array}\right. $$