방정식과 부등식 전체 문제

For the following exercises, use a system of linear equations with two variables and two equations to solve.

An investor earned triple the profits of what they earned last year. If they made $500,000.48 total for both years, how much did the investor earn in profits each year?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

If an investor invests a total of $25,000 into two bonds, one that pays 3% simple interest, and the other that pays $2\frac{7}{8}\%$ interest, and the investor earns $737.50 annual interest, how much was invested in each account?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

If an investor invests $23,000 into two bonds, one that pays 4% in simple interest, and the other paying 2% simple interest, and the investor earns $710.00 annual interest, how much was invested in each account?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

A store clerk sold 60 pairs of sneakers. The high-tops sold for $98.99 and the low-tops sold for $129.99. If the receipts for the two types of sales totaled $6,404.40, how many of each type of sneaker were sold?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

A concert manager counted 350 ticket receipts the day after a concert. The price for a student ticket was $12.50, and the price for an adult ticket was $16.00. The register confirms that $5,075 was taken in. How many student tickets and adult tickets were sold?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

Admission into an amusement park for 4 children and 2 adults is $116.90. For 6 children and 3 adults, the admission is $175.35. Assuming a different price for children and adults, what is the price of the child’s ticket and the price of the adult ticket?

If a given ordered triple solves the system of equations, is that solution unique? If so, explain why. If not, give an example where it is not unique.

If a given ordered triple does not solve the system of equations, is there no solution? If so, explain why. If not, give an example.

Using the method of addition, is there only one way to solve the system?

Can you explain whether there can be only one method to solve a linear system of equations? If yes, give an example of such a system of equations. If not, explain why not.

For the following exercises, determine whether the ordered triple given is the solution to the system of equations.

$\begin{array}{c}2x-6y+6z=-12 \\ \,x+4y+5z=-1 \\ -x+2y+3z=-1\,\end{array}$ and $(0,1,-1)$

For the following exercises, determine whether the ordered triple given is the solution to the system of equations.

$\begin{array}{c}\,6x-y+3z=6 \\ 3x+5y+2z=0\, \\ \,x+y=0\end{array}$ and $(3,-3,-5)$

For the following exercises, determine whether the ordered triple given is the solution to the system of equations.

$\begin{array}{c}6x-7y+z=2 \\ -x-y+3z=4\, \\ \,2x+y-z=1\end{array}$ and $(4,2,-6)$

For the following exercises, determine whether the ordered triple given is the solution to the system of equations.

$\begin{array}{c}x-y=0 \\ \,x-z=5 \\ x-y+z=-1\,\end{array}$ and $(4,4,-1)$

For the following exercises, determine whether the ordered triple given is the solution to the system of equations.

$\begin{array}{c}-x-y+2z=3 \\ \,5x+8y-3z=4 \\ -x+3y-5z=-5\,\end{array}$ and $(4,1,-7)$

For the following exercises, solve each system by elimination.

$\begin{array}{c}3x-4y+2z=-15 \\ \,2x+4y+z=16 \\ \,2x+3y+5z=20\end{array}$

For the following exercises, solve each system by elimination.

$\begin{array}{c}5x-2y+3z=20 \\ 2x-4y-3z=-9 \\ \,x+6y-8z=21\end{array}$

For the following exercises, solve each system by elimination.

$\begin{array}{c}\,5x+2y+4z=9 \\ -3x+2y+z=10 \\ \,4x-3y+5z=-3\end{array}$

For the following exercises, solve each system by elimination.

$\begin{array}{c}4x-3y+5z=31 \\ -x+2y+4z=20 \\ \,x+5y-2z=-29\end{array}$

For the following exercises, solve each system by elimination.

$\begin{array}{c}\,5x-2y+3z=4 \\ -4x+6y-7z=-1 \\ \,3x+2y-z=4\end{array}$