1. Select any two integers between -12 and +12 which will become solutions to a system of two equations.
2. Write two equations that have your two integers as solutions. Show how you built the equations using your integers. Your solution and equations should not be the same as those of other students or the textbook. There are infinite possibilities.
3. Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps. Use the example on page 357 of Mathematics in Our World as a guide.
4. Respond to at least two of your classmates’ postings. Do you agree or disagree that their examples model functions? Follow their 5 steps. Do their calculations follow the correct rules of algebra?
What equations did you select?
To answer this question, you should follow the steps below:
1. Select any two integers between -12 and +12. Let's select the integers 5 and -3.
2. Write two equations that have your two selected integers as solutions. Let's build the equations using the integers 5 and -3:
Equation 1: 2x + 3y = 7
Explanation: We can choose any coefficients for x and y, but the sum of the constants on both sides of the equation should be 7. Let's choose 2 as the coefficient for x and 3 as the coefficient for y.
Equation 2: 4x - 2y = -26
Explanation: Again, we can choose any coefficients for x and y, but the sum of the constants on both sides should equal -26. Let's choose 4 as the coefficient for x and -2 as the coefficient for y.
3. Solve the system of equations using the addition/subtraction method. Here are the 5 steps:
Step 1: Multiply one or both equations by a number to create opposite coefficients for one of the variables. In this case, Equation 1 can be multiplied by 2, which will result in:
4x + 6y = 14
Step 2: Add or subtract the equations to eliminate one variable. Subtract Equation 2 from the modified Equation 1:
(4x + 6y) - (4x - 2y) = 14 - (-26)
8y = 40
Step 3: Solve for the remaining variable. Divide both sides of the equation by 8:
y = 5
Step 4: Substitute the value of y into one of the original equations to solve for the other variable. Let's choose Equation 1:
2x + 3(5) = 7
2x + 15 = 7
2x = -8
x = -4
Step 5: Write the solution as an ordered pair. The solution to the system of equations 2x + 3y = 7 and 4x - 2y = -26 is (-4, 5).
4. Respond to at least two of your classmates' postings. Evaluate whether their examples model functions and whether their calculations follow the correct rules of algebra. Provide your agreement or disagreement and explain why.