Exam 11: Systems of Equations

Solve the system of equations by graphing the equations on the same set of axes. - $\left\{ \begin{array} { l } 3 x + y = 7 \\2 x + y = 4\end{array} \right.$

Solve the problem. -Two numbers total 10, and their difference is 16. Find the two numbers.

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? - $\left\{ \begin{array} { l } 2 x + y = 3 \\2 x + y = 1\end{array} \right.$

Decide whether or not the ordered pair satisfies the system of linear equations. -(-4, -7); $\left\{ \begin{array} { l } 2 x = - 15 - y \\x - 3 y = 17\end{array} \right.$

Solve the system of equations by graphing the equations on the same set of axes. - $\left\{ \begin{array} { l } y = - 5 x \\2 x - y = - 7\end{array} \right.$

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? - $\left\{ \begin{aligned}x & = - y \\y + x & = 5\end{aligned} \right.$

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

Write a system of equations to describe the situation. Do not solve the system. -Leroy has $14 less in his pocket than Zoe has. If Zoe had $5 more, she would have 2 times as much money as Leroy.

Solve the system by the substitution or the addition method. - $\left\{ \begin{array} { l } 3 ( 2 x + y ) = 3 x + 24 \\x - 2 y = - 1\end{array} \right.$

Without solving, choose the correct solution by deciding which choice satisfies the given conditions. -Rozlyn has two containers of water for a camping trip. One container holds 2 times as much as the other. The total amount of water is 18 gallons. How much water is in each container?

Solve the problem. -One number is four more than a second number. Two times the first number is 4 more than four times the second number.

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = 11 \\x - y = - 7\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{aligned}- 3 x - 5 y & = - 112 \\x & = 3 y\end{aligned} \right.$

Solve the problem. -Doreen and Irena plan to leave their houses at the same time, roller blade towards each other, and meet for lunch after 2 hours on the road. Doreen can maintain a speed of 6.6 miles per hour, which is 60% of Irena's Speed. If they meet exactly as planned, what is the distance between their houses?

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } y = 5 x - 7 \\y = 8 x - 6\end{array} \right.$

Solve the system by graphing. - $\left\{ \begin{array} { l } x - y = - 2 \\3 x - y = - 10\end{array} \right.$

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? - $\left\{ \begin{aligned}x + 5 y & = 20 \\y & = - \frac { 1 } { 5 } x + 4\end{aligned} \right.$

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 at least one solution is called a(n)_____________system.

Without solving, choose the correct solution by deciding which choice satisfies the given conditions. -Zacharias has a total of 61 coins, all of which are either dimes or nickels. The total value of the coins is $5.45. Find the number of each type of coin.

Solve the problem. -Chandra has 3 liters of a 24% solution of sodium hydroxide in a container. What is the amount and concentration of sodium hydroxide solution she must add to this in order to end up with 8 liters of 54% Solution?