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stealth61 [152]
3 years ago
5

Solve the system using the addition method. State your solution as an ordered pair.

Mathematics
1 answer:
vladimir1956 [14]3 years ago
6 0

Solution as ordered pair is:

(5,\frac{41}{2})

Step-by-step explanation:

Solving the system of equations:

3x+2y=56\,\,\,(1)\\9x-2y=4\,\,\,(2)

Adding equation(1) and equation(2)

3x+2y=56\\9x-2y=4\\--------\\12x=60\\x=\frac{60}{12}\\x=5

Putting value of x i.e x=5 in equation(1)

3x+2y=56\\3(5)+2y=56\\ 15+2y=56\\2y=56-15\\2y=41\\y=\frac{41}{2}\\y=\frac{41}{2}

So, value of x=5 and y=\frac{41}{2}

Solution as ordered pair is:

(5,\frac{41}{2})

Keywords:System of Equations

Learn more about System of Equations at:

  • brainly.com/question/6075514
  • brainly.com/question/7490805
  • brainly.com/question/13168205

#learnwithBrainly

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Let’s pretend that we want to give our employees in total a28% raise in the next two years, but we want to spread out aconsisten
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Solution

- The solution steps are given below:

\begin{gathered} \text{ Let the original amount be X} \\  \\ \text{ If we want a 28\% raise over the next two years, then it means that the amount will be:} \\ X+\frac{28}{100}X=1.28X \\  \\ \text{ If we want to give them a consistent raise each year, we can compute the scenario as follows:} \\ \text{ Let the percentage be }y \\  \\ X+y\%\text{ of }X=\text{ Salary after first year} \\  \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)\text{ = Salary after second year.} \\  \\ \text{ But we already know that the salary after second year is }1.28X \\ \text{ Thus, we can say:} \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)=1.28X \\  \\ \text{ Simplifying, we have:} \\ X+\frac{yX}{100}+\frac{y}{100}(X+\frac{yX}{100})=1.28X \\  \\ \text{ Divide through by }X \\ 1+\frac{y}{100}+\frac{y}{100}(1+\frac{y}{100})=1.28 \\  \\ \text{ Subtract 1 from both sides and expand the brackets} \\ \frac{y}{100}+\frac{y}{100}+(\frac{y}{100})^2=1.28-1=0.28 \\  \\ \frac{2y}{100}+(\frac{y}{100})^2=0.28 \\  \\ \text{ Multiply both sides by }100^2 \\ 200y+y^2=2800 \\  \\ \text{ Rewrite, we have:} \\ y^2+200y-2800=0 \\  \\ Solving\text{ the equation using the Quadratic formula, we have that:} \\ y=\frac{-200\pm\sqrt{200^2-4(-2800)}(1)}{2(1)} \\  \\ y=-213.137\text{   or   }13.137 \\  \\ \text{ Since the change in salary is an increase, thus, the rate }y\text{ has to be positive.} \\ \text{ Thus, } \\ y=13.137\approx13.14\% \\  \\  \end{gathered}

Final Answer

y = 13.14%

The screenshots of the solution are:

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