The flow chart shown below explains the steps to be done in solving system of linear equations with two unknowns 'x' and 'y' using elimination method.

**Example 1 : **

Solve by elimination method.

3x + 4y = -25

2x - 3y = 6

**Solution :**

3x + 4y = -25 ---- (1)

2x - 3y = 6 ---- (2)

Both x terms and y terms have different coefficients in the above system of equations.

Let's try to make the coefficients of y terms equal.

To make the coefficients of y terms equal, we have to find the least common multiple 4 and 3.

The least common multiple of 4 and 3 is 12.

Multiply the first equation by 3 in order to make the coefficient of y as 12 and multiply the second equation by 4 in order to make the coefficient of y as -12.

(1) ⋅ 3 ----> 9x + 12y = -75

(2) ⋅ 4 ----> 8x - 12y = 24

Now, we can add the two equations and eliminate y as shown below.

Divide each side by 17.

x = -3

Substitute -3 for x in (1).

(1)----> 3(-3) + 4y = -25

-9 + 4y = -25

Add 9 to each side.

4y = -16

Divide each side by 4.

y = -4

So, the values of x and y are -3 and -4 respectively.

**Example 2 :**

Solve by elimination method

2x + 3y = 5

3x + 4y = 7

**Solution :**

2x + 3y = 5 ----(1)

3x + 4y = 7 ----(2)

Both x terms and y terms have different coefficients in the above system of equations.

Let's try to make the coefficients of x terms equal.

To make the coefficients of y terms equal, we have to find the least common multiple 2 and 3.

The least common multiple of 2 and 3 is 6.

Multiply the first equation by 3 in order to make the coefficient of x as 6 and multiply the second equation by -2 in order to make the coefficient of x as -6.

(1) ⋅ 3 ----> 6x + 9y = 15

(2) ⋅ -2 ----> -6x - 8y = -14

Now, we can add the two equations and eliminate x as shown below.

Substitute 1 for y in (1).

(1)----> 2x + 3(1) = 5

2x + 3 = 5

Subtract 3 from each side.

2x = 2

Divide each side by 2.

x = 1

So, the values of x and y are 1 and 1 respectively.

**Example 3 : **

A park charges $10 for adults and $5 for kids. How many many adults tickets and kids tickets were sold, if a total of 548 tickets were sold for a total of $3750 ?

**Solution : **

**Step 1 :**

Let "x" be the number of adults tickets and "y" be the number of kids tickets.

No. of adults tickets + No. of kids tickets = Total

x + y = 548 ----(1)

**Step 2 : **

Write an equation which represents the total cost.

Cost of "x" no. adults tickets = 10x

Cost of "y" no. of kids tickets = 5y

Total cost = $3750

Then, we have

10x + 5y = 3750

Divide both sides by 5.

2x + y = 750 ----(2)

**Step 3 :**

Solve (1) and (2) using elimination method.

x + y = 548 ----(1)

2x + y = 750 ----(2)

In the above two equations, y is having the same coefficient, that is 1.

Multiply the first equation by -1 to get the coefficient of -1. And keep the second equation as it is.

Then, we have

-x - y = - 548

2x + y = 750

We can add the above two equations and eliminate y.

Then, we have

x = 202

**Step 4 : **

Substitute 202 for x in the first equation.

(1)----> 202 + y = 548

Subtract 202 from each side.

y = 346

So, the number of adults tickets sold is 202 and the number of kids tickets sold is 346.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**