Solving Systems of Equations

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Solving Systems of Equations
In mathematics, system of equation is one important topic. A set of linear equations contains a solution set
which is common called Solving system of equations. In a linear equation with two variables are in the
standard form of ax + by + c = 0. Where x and y are variables and a, b, and c are real numbers and also a ? 0
and b ? 0 in the standard form. Example for two variable linear equation is 4x + 5y = 20. Let us see some
example problems for solving systems of equation.
Solve Systems of Equations
Steps to Solving system of equations using the substitution method are
Step 1:
Given system of equation with two variable
Step 2:
Take the first equations
Step 3:
Eliminate one variable
Step 4:
Substitute the values of that variable in the any equation
Step 5:
x and y values are obtained.
Examples to Solve Systems of Equations
Example 1:
Solving the systems of equations by using the substitution method
4x + 2y = 6


2x - 6y = 24
Solution:

Step 4:
Substitute the b = 9 - 3a in (2) we get
4a - b = 5
4a - (9 - 3a) = 5
4a - 9 + 3a = 5
4a + 3a = 5 + 9
7a = 14
a = 2
Step 5:
Substitute the a = 2 in (1) we get
3a + b = 9
3(2) + b = 9
6 + b = 9
b = 9 - 6
b = 3
Step 6:
Answer:
a = 2
b = 3
Practice Problems to Solve Systems of Equations
Problem 1:
Solving the Solving system of equationsy using the substitution method
2x + 6y = 6
-2x + 2y = -6
Solution:
x = 3
y = 0
Problem 2:
Solving the systems of equations by using the substitution method
5a + 7b = -25
11a + 6b = -8
Solution:


a = 2
b = -5

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