Hi friends, I am going to discuss about how to graph linear equations?
Linear equation is a pair of equation in two variables. There are two types of linear equations. First one is simultaneous linear equation of two variables and second one is graphical representation of linear equation. In this session, we will be discussing solving linear equations with two variables and solving simple problems from different areas.
In general form a linear equation in two variables x and y is
a1x+b1y+c1=0
a2x+b2y+c2=0
where a1, b1, c1 and a2, b2, c2 are all real numbers and x, y are variables. This is known as the algebraic representation of linear equation in two variables.
We take some examples of linear equation.
Example 1:- Show that x=2, y=1 is a solution of the simultaneous linear equations.
3x-2y=4
2x+y=5
solution :- the given system of equation is
3x-2y=4
2x+y=5
putting the x=2 and y=1 in equation (1) we have
L.H.S= 3*2-2*1=4= R.H.S
putting the x=2 and y=1 in equation (11) we have
L.H.S=2*2+1*1=5=R.H.S
thus, x=2 and y=1 and this satisfies both the equations of the given system.
Hence, x=2 and y=1 is a solution of the given system.
Now, we discuss about linear equation with fraction such that express by x/y.
We take some example to solving linear equations with fractions
Example 1:- solution equation (x+1)/3 =(2x+1)/5 solving by linear equation with fraction.
Solution :- to solve the equation step1:- (x+1)/3 =(2x+1)/5
step 2:- (x+1)/3 =(2x+1)/5 (we can start with left side and we can use cross multiply it means to one multiply numerator of one fraction by denominator of another fraction).
Step 3 :- 3(2x+1) = 5(x+1)
step 4:- 6x+3 =5x+5
step 5:- 6x-5x = 5-3
step 6:- x = 2 (this is answer for x)
now, we can check this solution putting the x = 2 in equation (1) we have
step 1:- L.H.S = (2+1)/3 =3/3 = 1
now, again putting the x = 2 in equation (2) we have
step :- R.H.S = (2*2+1)/5 =5/5 =1
so, L.H.S =R.H.S
In upcoming posts we will discuss about Substitution Method to Solving Simultaneous Equations and Congruent Triangles. Visit our website for information on CBSE board fashion studies syllabus for class 11
Linear equation is a pair of equation in two variables. There are two types of linear equations. First one is simultaneous linear equation of two variables and second one is graphical representation of linear equation. In this session, we will be discussing solving linear equations with two variables and solving simple problems from different areas.
In general form a linear equation in two variables x and y is
a1x+b1y+c1=0
a2x+b2y+c2=0
where a1, b1, c1 and a2, b2, c2 are all real numbers and x, y are variables. This is known as the algebraic representation of linear equation in two variables.
We take some examples of linear equation.
Example 1:- Show that x=2, y=1 is a solution of the simultaneous linear equations.
3x-2y=4
2x+y=5
solution :- the given system of equation is
3x-2y=4
2x+y=5
putting the x=2 and y=1 in equation (1) we have
L.H.S= 3*2-2*1=4= R.H.S
putting the x=2 and y=1 in equation (11) we have
L.H.S=2*2+1*1=5=R.H.S
thus, x=2 and y=1 and this satisfies both the equations of the given system.
Hence, x=2 and y=1 is a solution of the given system.
Now, we discuss about linear equation with fraction such that express by x/y.
We take some example to solving linear equations with fractions
Example 1:- solution equation (x+1)/3 =(2x+1)/5 solving by linear equation with fraction.
Solution :- to solve the equation step1:- (x+1)/3 =(2x+1)/5
step 2:- (x+1)/3 =(2x+1)/5 (we can start with left side and we can use cross multiply it means to one multiply numerator of one fraction by denominator of another fraction).
Step 3 :- 3(2x+1) = 5(x+1)
step 4:- 6x+3 =5x+5
step 5:- 6x-5x = 5-3
step 6:- x = 2 (this is answer for x)
now, we can check this solution putting the x = 2 in equation (1) we have
step 1:- L.H.S = (2+1)/3 =3/3 = 1
now, again putting the x = 2 in equation (2) we have
step :- R.H.S = (2*2+1)/5 =5/5 =1
so, L.H.S =R.H.S
In upcoming posts we will discuss about Substitution Method to Solving Simultaneous Equations and Congruent Triangles. Visit our website for information on CBSE board fashion studies syllabus for class 11
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