Grade 10 Math Elimination

Introduction to Grade 10 math elimination:

Elimination method is used to solve if we have two unknown variables. In grade 10 math elimination we are going to solve word problems. In grade 10 math elimination problems we have to use the multiplication operation to eliminate the variables. After eliminating we will get the equation with one variable. Using that we have to find the x and y values. Here we will see an example problem for grade 10 math elimination method.

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Example problems grade 10 math elimination methods:


Example:

Solve the following equation using elimination method.

5x + y = 10

2x + 3y = - 9

Solution:

Given equations are,

5x + y = 10    ………………… (1)

2x + 3y = - 9     ...……………....  (2)

Here both variables having different co – efficient. So multiply the first equation with 3 for eliminating y.

15x + 3 y = 30   …………………. (3)

2x + 3 y = - 9    ………………… (4)

Now subtract 3 and 4

We get,

13x = 39

Now we have to divide by 13 on both side of the equation,

So x = 3

Now plug the value in any of the equation.

5(3) + y = 10

15 + y = 10

So y = - 5

In this the variables with values given in the equation directly. Now we will see an example to make an equation and then we have to solve.

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Example 2:


Alex and Jerry is have the total age is 30. Three years ago, the sum of twice Alex's age and three times Tom's age was 60 years. Find both of their ages using elimination method.

Solution:

Sum of Alex and Jerry’s age is 30

x + y = 30 ……………….. (1)

Three years ago gives x -3 and y – 3

2 (x – 3) + 3 (y – 3) = 60

2x – 6 + 3y – 9 = 60

2x + 3y - 15 = 60

2x + 3y = 75    ……………………. (2)

Multiply (1) with 2

2x + 2y = 60   .......................... (3)

2x + 3y = 75    ......................... (4)

Now subtract the equation

We get,

-y = - 15

So y = 15 (Jerry’s age)

From this Alex’s age x + 15 = 30 than x = 15

So Alex age = 15 and Jerry’s age = 15

These are the some example problems for grade 10 math elimination.