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 Question: Modelling 5 separate equations into 1 equation
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Modelling 5 separate equations into 1 equation
To model 5 separate equations into 1 equation, you can use a system of equations.
Let’s say we have 5 equations:
a + b = c
2a – 3b = d
3a + 4b = e
a – b = f
4a + 2b = g
To model these 5 equations into 1 equation, we can represent them in a matrix form as follows:
 1 1   a   c 
 2 3   b  =  d 
 3 4     e 
 1 1     f 
 4 2     g 
This can be written as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
To solve for X, we can use matrix algebra to find the inverse of A and then multiply it with B. The resulting X matrix will contain the values of a and b that satisfy all 5 equations.
Once you have found X, you can substitute the values of a and b into any one of the original equations to get a single equation that models all 5 equations.
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Is 5x 3y 5 a linear equation in one variable?
No, 5x 3y 5 is not a linear equation in one variable.
A linear equation in one variable is an equation that can be written in the form of ax + b = 0 or ax = b, where a and b are constants and x is the variable.
The given equation, 5x 3y 5, has two variables, x and y, and it cannot be simplified to the form of a linear equation in one variable. Therefore, it is not a linear equation in one variable.
What are the 5 steps of solving a linear equation in two variables strategy?
The 5 steps to solve a linear equation in two variables are as follows:

Simplify both sides of the equation by combining like terms: The first step is to simplify the equation by combining like terms. For example, if the equation is 2x + 3y = 7, you would add the 2x and 3y terms together to get 2x + 3y = 7.

Move the variable terms to one side of the equation: Next, move all the variable terms (the terms with x and y) to one side of the equation. For example, if the equation is 2x + 3y = 7, you would subtract 2x from both sides to get 3y = 2x + 7.

Divide both sides by the coefficient of the variable: After moving the variable terms to one side of the equation, divide both sides by the coefficient of the variable. For example, if the equation is 3y = 2x + 7, you would divide both sides by 3 to get y = (2/3)x + 7/3.

Repeat steps 13 for the other variable: If you want to solve for the other variable (in this case x), repeat steps 13 for that variable.

Check your solution: Finally, check your solution by substituting the values you found for x and y back into the original equation. If both sides of the equation are equal, then your solution is correct.
What are the 5 steps to solving linear equations with variables on both sides?
Here are the five steps to solving linear equations with variables on both sides:

Simplify both sides of the equation by combining like terms.

Move all the variable terms to one side of the equation by adding or subtracting the same term from both sides.

Move all the constant terms to the other side of the equation by adding or subtracting the same term from both sides.

Simplify both sides of the equation again by combining like terms.

Solve for the variable by dividing both sides of the equation by the coefficient of the variable, if necessary.
Here is an example of these steps in action:
2x + 3 = 5x – 2
Step 1: Simplify both sides by combining like terms:
2x – 5x = 3 – 2
Step 2: Move all the variable terms to one side of the equation:
3x = 5
Step 3: Move all the constant terms to the other side of the equation:
3x + 3 = 2
Step 4: Simplify both sides of the equation again by combining like terms:
3x = 2 – 3
Step 5: Solve for the variable by dividing both sides of the equation by the coefficient of the variable:
x = (2 – 3) / 3
x = 5/3
Therefore, the solution to the equation 2x + 3 = 5x – 2 is x = 5/3.
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