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Exam 11: Systems of Equations

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Question 41

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Solve the system by the substitution or the addition method. - $\left\{ \begin{array} { l } x + \frac { 1 } { 51 } y = 3 \\- 3 x + 2 y = 12\end{array} \right.$

A) $\left( 2 \frac { 4 } { 5 } , 10 \frac { 1 } { 5 } \right)$
B) $\left( 4 \frac { 4 } { 5 } , 8 \frac { 1 } { 5 } \right)$
C) (2, -3)
D) $\left( \frac { 1 } { 51 } , 1 \right)$

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Question 42

Multiple Choice

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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 the same, the equations are_____________ equations.

A) inconsistent
B) dependent
C) independent
D) addition

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Question 43

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Decide whether or not the ordered pair satisfies the system of linear equations. -(-6, 5); $\left\{ \begin{array} { l } x + y = - 1 \\x - y = - 11\end{array} \right.$

Answer true or false. -Although (7, 3)is not a solution of x + 3y = 2, it can still be a solution of the system $\left\{ \begin{array} { l } x + 3 y = 2 \\x + y = 4\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { r } x + 8 y = - 39 \\2 x + 8 y = - 46\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 3 x - 5 y = - 7 \\3 x - 5 y = 8\end{array} \right.$

Is the ordered pair a solution of the linear system? - $\left\{ \begin{array} { l } 2 x - 4 y = 6 \\5 x + y = 1\end{array} ; ( 1 , - 1 ) \right.$

Answer true or false. -If the two equations in a system of linear equations are added and the result is 7x = 0, the system has no solution.

Solve the problem. -The three angles in a triangle always add up to 180°. If one angle in a triangle is 114° and the second is 5 times the third, what are the three angles?

Solve the system of equations by the addition method. - $\left\{ \begin{array} { r r } 7 x + 2 y = & 9 \\- 2 x - 2 y = & - 24\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = 33 \\x - y = 13\end{array} \right.$

Without graphing, decide: (a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point? (b) How many solutions does the system have? - $\left\{ \begin{aligned}3 x - y & = 1 \\x + 4 y & = 22\end{aligned} \right.$

Answer true or false. -If the two equations in a system of linear equations are added and the result is 8 = 0, the system has no solution.

Decide whether or not the ordered pair satisfies the system of linear equations. -(2, -6); $\left\{ \begin{array} { l } 4 x + y = 2 \\2 x + 4 y = - 20\end{array} \right.$

Is the ordered pair a solution of the linear system? - $\left\{ \begin{array} { l } 5 x - 3 y = 21 \\4 x + 5 y = - 3\end{array} ; \quad ( 3 , - 2 ) \right.$

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

Solve the problem. -Julie and Eric row their boat (at a constant speed) 35 miles downstream for 5 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 7 hours. Find the rate of the current.

Decide whether or not the ordered pair satisfies the system of linear equations. -(3, -1); $\left\{ \begin{array} { l } x + y = - 4 \\x - y = - 2\end{array} \right.$

Solve the system of equations by graphing the equations on the same set of axes. - $\left\{ \begin{array} { l } x + y = 1 \\x - y = 5\end{array} \right.$

Write a system of equations to describe the situation. Do not solve the system. -One number is 5 more than another number. If you add 9 to 2 times the first number, the result is 3 times the second number.