Introduction to two equations and two unknowns:
Two linear equations in the same two variables (unknowns) are called a pair of linear equations in two variables. The most general form of a pair of linear equations is
a1x+b1y+c1=0
a2x+b2y+c2=0
An example of linear system involves two equations and two unknowns:
x+ y=3 and x - y=2
There are the methods used to solve two unknowns with two equations:
Substitution method
Elimination method
Graphing method
Here, we are going to see the problems on two equations and two unknowns by substitution and elimination method.
Two Equations Two Unknowns-solving
Example problem 1:
Solve for the two variables x and y from the following two equations:
3x+y=5
y+5x=2
Solution:
Here, we have to solve the pair of equations with two unknowns by substitution method.
Step 1: We pick any one of the equations and write one variable in terms of the other.
Let us consider the Equation (1):
3x+y=5
Subtract 3x on both sides of the equation
3x+y-3x=5-3x
y=5-3x------------------------Equation (3)
Step 2: Substitute the value of y in Equation (2). We get
y+5x=2
5-3x+5x=2
5+2x=2
Subtract 5 on both sides
2x=2-5
2x=-3
Divide by 2 on both sides of the equation
2x/2=-3/2
x=-1.5
Step 3: Plugging this value of x in Equation (3), we get
y=5-3x
y=5-3(-1.5)
y=5+4.5
y=9.5
So, the solution of two unknowns is (-1.5, 9.5).
Algebra is widely used in day to day activities watch out for my forthcoming posts on algebra math problem solver and solving algebraic proportions. I am sure they will be helpful.
Two Equations Two Unknowns- by Elimination Method:
Example problem 2: Solve for the two variables x and y from the following two equations:
9x – 4y = 2000----------Equation (1)
7x – 3y = 2000----------Equation (2)
Solution:
We have to solve the pair of equations by Elimination method.
Step 1: Equation (1) is multiplied by 3 and Equation (2)is multiplied by 4 to make the coefficients of y equal. Then we get the equations:
27x – 12y = 6000------Equation (3)
28x – 12y = 8000------Equation (4)
Step 2: Equation (3) is subtracted from Equation (4) to eliminate y, because the coefficients
of y are the same. So, we get
(28x – 27x) – (12y – 12y) = 8000 – 6000
i.e., x = 2000
Step 3: Substituting this value of x in (1), we get
9(2000) – 4y = 2000
i.e., y = 4000
So, the solution of two unknowns is (2000, 4000).
Two linear equations in the same two variables (unknowns) are called a pair of linear equations in two variables. The most general form of a pair of linear equations is
a1x+b1y+c1=0
a2x+b2y+c2=0
An example of linear system involves two equations and two unknowns:
x+ y=3 and x - y=2
There are the methods used to solve two unknowns with two equations:
Substitution method
Elimination method
Graphing method
Here, we are going to see the problems on two equations and two unknowns by substitution and elimination method.
Two Equations Two Unknowns-solving
Example problem 1:
Solve for the two variables x and y from the following two equations:
3x+y=5
y+5x=2
Solution:
Here, we have to solve the pair of equations with two unknowns by substitution method.
Step 1: We pick any one of the equations and write one variable in terms of the other.
Let us consider the Equation (1):
3x+y=5
Subtract 3x on both sides of the equation
3x+y-3x=5-3x
y=5-3x------------------------Equation (3)
Step 2: Substitute the value of y in Equation (2). We get
y+5x=2
5-3x+5x=2
5+2x=2
Subtract 5 on both sides
2x=2-5
2x=-3
Divide by 2 on both sides of the equation
2x/2=-3/2
x=-1.5
Step 3: Plugging this value of x in Equation (3), we get
y=5-3x
y=5-3(-1.5)
y=5+4.5
y=9.5
So, the solution of two unknowns is (-1.5, 9.5).
Algebra is widely used in day to day activities watch out for my forthcoming posts on algebra math problem solver and solving algebraic proportions. I am sure they will be helpful.
Two Equations Two Unknowns- by Elimination Method:
Example problem 2: Solve for the two variables x and y from the following two equations:
9x – 4y = 2000----------Equation (1)
7x – 3y = 2000----------Equation (2)
Solution:
We have to solve the pair of equations by Elimination method.
Step 1: Equation (1) is multiplied by 3 and Equation (2)is multiplied by 4 to make the coefficients of y equal. Then we get the equations:
27x – 12y = 6000------Equation (3)
28x – 12y = 8000------Equation (4)
Step 2: Equation (3) is subtracted from Equation (4) to eliminate y, because the coefficients
of y are the same. So, we get
(28x – 27x) – (12y – 12y) = 8000 – 6000
i.e., x = 2000
Step 3: Substituting this value of x in (1), we get
9(2000) – 4y = 2000
i.e., y = 4000
So, the solution of two unknowns is (2000, 4000).
