I am stuck on trying to figure out how to do this question. Could someone please show me 5 necessary steps ? Thank you. Here is how the assignment question is worded.

Question

I am stuck on trying to figure out how to do this question. Could someone please show me 5 necessary steps ? Thank you. Here is how the assignment question is worded.

Select any two integers between -12 and +12 which will become solutions to a system of two equations.
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.
Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps.

Answer 1

I will try it with x=20, y=15

From this, you can supply coefficients and calculate the right hand side from the given values of x and y.

I choose coefficients 2 and -3 to give
2x-3y=2*20-3*15=-5
I choose again coefficients, 3 and -1 to give
3x-y=3*20-1*15=45

So my equations are
2x-3y=-5
3x-y=45

Then I would proceed to solve for x and y, which should give me x=20 and y=15, as expected.

Answer 2

Correct Math Mate :3

Answer 3

WHOO NICE WORK HUMANS

Answer 4

Sure! Here are five necessary steps to solve this problem using the addition/subtraction method:

Step 1: Start by selecting two integers between -12 and +12. Let's say we choose 5 and -3. These will be the solutions to our system of equations.

Step 2: Write two equations that have your chosen integers as solutions. To build the equations, you can use any mathematical operations involving the integers. Let's create two equations as examples:

Equation 1: 2x + y = 7
Equation 2: 3x - y = -18

Step 3: Now that we have our equations, we need to solve the system by the addition/subtraction method. The goal is to eliminate one variable by adding or subtracting the equations.

In this example, we will eliminate the 'y' variable. To do this, we'll multiply Equation 1 by 1 and Equation 2 by 2. This will create opposite coefficients for 'y'.

Equation 1 (multiplied by 1): 2x + y = 7
Equation 2 (multiplied by 2): 6x - 2y = -36

Step 4: Next, add the two modified equations together. This will eliminate the 'y' variable.

(Equation 1 + Equation 2):
2x + y + 6x - 2y = 7 - 36

Simplify the equation:
8x - y = -29

Step 5: Now we have a new equation with only one variable, 'x'. Solve for 'x' by isolating the variable on one side.

Add 'y' to both sides of the equation:
8x - y + y = -29 + y

Simplify:
8x = -29 + y

Divide both sides by 8:
x = (-29 + y) / 8

Since we are given that x should be an integer, we can substitute our chosen value of 'y' (-3) and solve for 'x':
x = (-29 + (-3)) / 8
x = (-29 - 3) / 8
x = -32 / 8
x = -4

So, by using the addition/subtraction method, we found that the values of 'x' and 'y' that satisfy the system of equations 2x + y = 7 and 3x - y = -18 are x = -4 and y = -3.

Please note that the equations and solutions provided here are just one possible example, and there are infinitely many combinations of equations and solutions that would meet the given requirements.