Exam 10: Systems of Equations

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { c } 4 x - y = 5 \\8 x + 6 y = 2\end{array} \right)$

Use the addition method to solve the system. $\left\{ \begin{array} { c } a + b = 3 \\a - b = - 1\end{array} \right.$

Solve the system. $\left\{ \begin{array} { l } x + y = 2 \\x - y = 0\end{array} \right.$

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } 10 a - 3 b = 1 \\5 a - 10 c = 1 \\2 b - 10 c = 0\end{array} \right.$

Find the solution set of the system of inequalities. $\left\{ \begin{array} { c } x - y \geq 6 \\x + 2 y < - 4\end{array} \right.$

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { c } 6 x - 2 y = 6 \\12 x - 4 y = - 5\end{array} \right)$

Solve the system of equations by graphing. $\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 68 \\y = 2 x ^ { 2 }\end{array} \right.$

Use two equations in two variables to solve the following problem. At a theater, the giant rectangular movie screen has a width $24$ feet less than its length. If its perimeter is $308$ feet, find the area of the screen.

Solve using substitution: $\left\{ \begin{array} { c } x - 4 z = 7 \\7 x + y + 6 z = 84 \\y + 3 z = 9\end{array} \right.$

Solve the system of equations by graphing. $\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 25 \\52 x ^ { 2 } + 13 y ^ { 2 } = 676\end{array} \right.$

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 9 ( x - 1 ) + 41 = 75 - 7 y \\7 ( x + 1 ) + 29 = 68 - 4 y\end{array} \right.$

Part of $7,000 is invested at 10%, another part at 11%, and the remainder at 12% yearly interest. The total yearly income from the three investments is $795. The sum of the amounts invested at 10% and 11% equals the amount invested at 12%. How much is invested at each rate?

Part of $3,800 is invested at 12%, another part at 13%, and the remainder at 14%. The total yearly income from the three investments is $506. The sum of the amounts invested at 12% and 13% equals the amount invested at 14%. Determine how much is invested at each rate.

Solve the system. Give your answer as an ordered triple in the form of ( a, b, c ). $\left\{ \begin{array} { c } 8 a - 3 b = 1 \\6 a - 10 c = 1 \\2 b - 8 c = 0\end{array} \right.$

Use two equations in two variables to find the following integers. Twice one integer plus another integer is 19. The first integer plus 3 times the second is 32.

Solve the system. $\left\{ \begin{array} { c } 3 x - 6 y = 18 \\x = 2 y + 3\end{array} \right.$

Find the solution set of the system of inequalities. $\left\{ \begin{array} { l } x + y < - 6 \\x - y > - 6\end{array} \right.$

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { l } \frac { 1 } { 4 } x - \frac { 1 } { 20 } y = 10 \\\frac { 1 } { 4 } x + \frac { 1 } { 8 } y = - 11\end{array} \right)$

Find the solution set of the system of inequalities. $\left\{ \begin{array} { c } 5 x + 3 y > - 8 \\4 x - 5 y \geq 1\end{array} \right.$

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. $\left\{ \begin{array} { l } 2 ( x - 4 ) = 8 y \\4 ( 2 y + 2 ) = 2 x\end{array} \right.$