Exam 11: Systems of Equations

The double line graph below shows the number of Acme Superstores vs. the number of General Superstores. -In what year was the number of Acme stores approximately equal to the number of General stores?

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } 4 y = x + 40 \\2 x + 8 y = 0\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } - 6 y + 7 y = - 1 x + 2 ( x - 3 ) + 1 x + 3 \\5 ( x + y ) - x + y = - 2\end{array} \right.$

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -In a system of linear equations in two variables, if the graphs of the equations are different, the equations are_____________ equations.

Solve the problem by writing and using a system of linear equations. -Two numbers have a sum of 120 and a difference of 54. Find the numbers.

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -A(n)_____________of a system of two equations in two variables is an ordered pair of numbers that is a solution of both equations in the system.

Decide whether or not the ordered pair satisfies the system of linear equations. - , 2x=6-y x-10y=-8

Solve the problem. -The sum of two numbers is 6. Five times the first number equals 2 times the second number. Find the two numbers.

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 2 x + 3 y = 14 \\3 x + 5 y = 19.2\end{array} \right.$

Solve the system by the substitution or the addition method. - $\left\{ \begin{array} { l } 25 x - 5 y = 15 \\y = 5 x - 3\end{array} \right.$

Solve the problem. -Khang and Hector live 32.4 miles apart in southeastern Missouri. They decide to bicycle towards each other and meet somewhere in between. Hector's rate of speed is 80% of Khang's. They start out at the same time and meet 3 hours later. Find Hector's rate of speed.

Solve the system by the substitution or the addition method. - $\left\{ \begin{array} { l } \frac { x + 1 } { 2 } = \frac { 3 - y } { 4 } \\\frac { - 1 - 2 x } { 3 } = \frac { y } { 1 }\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } x - 7 y = 1 \\- 3 x - 8 y = - 32\end{array} \right.$

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -A system of equations that has no solution is called a(n)_____________system.

Solve the system of equations by graphing the equations on the same set of axes. - $\left\{ \begin{array} { l } x = - 3 \\y = - 3\end{array} \right.$

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -Two or more linear equations are called a(n)_____________.

Solve the problem. -Dmitri needs 6 liters of a 46% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 54% solution and the other an unlimited Supply of the 30% solution. How many liters of each solution should Dmitri use?

Solve the problem. -On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $5 each and a number of necklaces at $15 each. She wrote a check for $1400 to pay for the order. How many bracelets And how many necklaces did Rosaria purchase?

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } 4 x - 3 y = - 15 \\y = x + 4\end{array} \right.$

Solve the problem. -Jimmy is a partner in an Internet-based coffee supplier. The company offers gourmet coffee beans for $14 per pound and regular coffee beans for $5 per pound. Jimmy is creating a medium-price product that will sell for $7 per pound. The first thing to go into the mixing bin was 10 pounds of the gourmet beans. How many pounds Of the less expensive regular beans should be added?