In this section, you will learn how to solve linear linear equations in two variables using the concept substitution.

We use the following steps to solve a system of linear equations.

**Step 1 :**

Solve one of the equations for one of its variables.

**Step 2 :**

Substitute the expression from step 1 into the other equation and solve for the other variable.

**Step 3 :**

Substitute the value from step 2 into either original equations and solve for the variable in step 1.

**Problem 1 :**

Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of "m" for which y = mx + 3.

**Solution :**

2x + 3y = 11 ----------- (1)

2x - 4y = -24 ----------- (2)

**Step 1 :**

Find the value of one variable in terms of other variable

3y = 11 - 2 x

y = (11 - 2 x)/3

Let us apply the value of y in (2),

2x - 4(11 - 2x)/3 = -24

14x - 44 = -24 (3)

14x - 44 = -72

14x = -72 + 44

14x = - 28

Divide 14 on both sides, we get

x = -2

Substitute x = -2 in the equation y = (11 - 2 x)/3

y = [11 - 2(-2)]/3

y = 15/3

y = 5

Now we have to apply these values in the equation

y = m x + 3

5 = m (-2) + 3

5 = -2 m + 3

-2m = 2

-2 m = 2

m = 2/(-2)

m = -1

**Problem 2 :**

Form the pair of linear equations of the following problems and find their solution by substitution method.

(i) The difference between two numbers is 26 and one number is three times the other. Find them

**Solution :**

Let the two numbers are "x" and "y"

Difference between two number is 26

x - y = 26 -------- (1)

One number is three times the other

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

Let us apply (2) in (1)

3 y - y = 26

2 y = 26

Divide by 2 on both sides, we get

y = 13

By applying the value of y in (2), we get

x = 3 (13)

x = 39

So, required two numbers are 39 and 13.

**Problem 3 :**

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them

**Solution :**

Let the two supplementary angles are "x" and "y"

Sum of these two angles is 180

x + y = 180 -----(1)

the larger angle exceeds the smaller by 18

x = y + 18 -----(2)

Now,we are going to apply the value of x in the first equation

y + 18 + y = 180

2y = 180 - 18

2y = 162

y = 162/2

y = 81

x = 81 + 18

x = 99

So, two supplementary angles are 99 and 81.

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

HTML Comment Box is loading comments...

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**