Elimination Using Addition and Subtraction

Minggu, 16 Juli 2023

Another algebraic method for solving systems of equations is called elimination. You can eliminate one of the variables by adding or subtracting the equations.

Use elimination when the coefficients of one of the variables are equal or additive inverses. For example, consider the system below.

5x + 11y = 12                  2x + 11y = 36

Notice that the coefficient of y in both equations is the same. You can solve this system of equations in three steps.

Example

 

1.    Use elimination to solve the system of equations.

2x + y = 3

x + y = 1

 

Alternative Solutions:

 

Now substitute in either equation to find the value of y. Choose the equation that is easier for you to solve.

The solution of the system of equations is (2, –1).

 

Check:

 

Example

Entertainment Link

 

2.   A group of 3 adults and 10 students paid $102 for a cavern tour. Another group of 3 adults and 7 students paid $84 for the tour. Find the admission price for an adult and for a student.

 

Alternative Solutions:

 

Let a = the price for an adult and s = the price for a student.

Write two equations to represent this situation.

Now substitute in either equation to find the value of a.

The solution of the system of equations is (14, 6). This means that the cost for adults was $14 and the cost for students was $6.

 

Check:

 

In some systems of equations, the coefficients of one of the variables are additive inverses. For these systems, apply the elimination method by adding the equations.

 

Example

 

3.    Use elimination to solve the system of equations.

4x – 6y = 10

3x + 6y = 4

 

Alternative Solutions:

 

Now substitute x into either equation to find the value of y.

The solution of the system is . Check this result.

 

Systems of equations can be used to solve digit problems. Digit problems explore the relationships between digits of a number.

 

Example

Number Theory Link

 

4.   The sum of the digits of a two-digit number is 8. If the tens digit is 4 more than the units digit, what is the number?

 

Alternative Solutions:

 

Let t represent the tens digit and let u represent the units digit.

Rewrite the second equation so that the t and u are on the same side of the equation.

t = u + 4           →      t – u = 4

Then use elimination to solve.

Now substitute to find the units digit.

     

 

Since t is 6 and u is 2, the number is 62. Check this solution.

 

 

Sumber

Labels: Mathematician

Thanks for reading Elimination Using Addition and Subtraction. Please share...!