Exam 3: Systems of Equations

Solve the system. If the system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } x + y + z = 6 \\2 x + y - z = 7 \\2 x - 3 y + z = 1\end{array} \right.$

A merchant wishes to mix peanuts that sell for $3 a pound and cashews that sell for $6 a pound to get 70 pounds of mixed nuts that sell for $5 a pound. How many pounds of peanuts should the merchant use? ________ pounds of peanuts

Explain why the following problem does not give enough information to answer the question. The sum of three integers is 48. If the second integer is doubled, the sum is 63. Find the integers.

The sum of the angles in any triangle is 180∘ . In triangle ABC , angle A is 100∘ less than the sum of angles B and C , and angle C is 100∘ less than twice angle B . Find each angle. A = __________ ∘ , B = __________ ∘ , C = __________ ∘

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 3 x + 4 y = 2 \\9 x - 2 y = 20\end{array} \right.$

The system of equations $a + b i$ will be solved by substitution. If substituting the expression for y in equation 1 into equation 2, the new equation is

Explain why the following problem does not give enough information to answer the question: The sum of three integers is 48. If the first integer is doubled, the sum is 67. Find the integers.

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } x + y + z = 7 \\x + y - z = 5 \\x - y + z = 1\end{array} \right.$

How many liters of a 40% alcohol solution must be mixed with 30 liters of a 70% solution to get a 55% solution?

Solve the system by any method, if possible. Give your answer in the form of ( m, n) . $\log _ { 5 } 9$

A(n) ___________ is a number that is associated with a square matrix.

A(n) __________ is a rectangular array of numbers written within brackets.

Use the graphs in the illustration to solve the equation. $- x - 3 = x - 1$ $y = - 2 x + 1$ $y = - x - 3$ $y = x - 1$ $x =$ __________

Which of the following evaluates the determinant $\left| \begin{array} { c c c } 6 & - 3 & 4 \\5 & 7 & - 5 \\8 & 2 & 6\end{array} \right|$ by expanding by row 2?

Determine if $\left( 4 , - \frac { 1 } { 3 } \right)$ is a solution of the system $\left\{ \begin{array} { l } 5 x - 3 y = 21 \\\frac { 1 } { 2 } x - 3 y = 3\end{array} \right.$

Without graphing, how can you tell that the graphs of $y = 4 x - 5 \text { and } y = 5 x + 6$ intersect?

Suppose that the three countries that won the most medals in the recent Winter Olympics together won a total of 95 medals. The first country's medal count was seven more than the seconds' and the second country's medal count was 2 more than third's. Find the number of medals won by each country.

For the system $\left\{ \begin{array} { l } 2 x + 3 y = 1 \\5 x - y = 5\end{array} \right.$ , $D _ { x } = - 16$ , $D _ { y } = 5$ and $D = - 17$ . What is the solution of the system?

A piece of cheese toast has 111 calories. The bread has fifteen more calories than the cheese. Find the number of calories in the bread. ________ calories in bread

Solve the system by any method, if possible. If the system is inconsistent, or if the equations are dependent, so indicate. $a + b i$