system of equation substitution method

System of Equation 

Free Math Education (Algebra Math) Students learn to solve systems of equations by substitution by first isolating a variable in one of the equations in the system, then substituting its value for the corresponding variable in the other equation. You can also learn to solve the equations by the method of their choice using the following rules: 

if one of the variables cancels out when the equations are added together, then use addition, and if a variable is already isolated in one of the equations, use substitution method.

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step by step solution substitution method

Substitution Method

 

Calculate value of x and y: Equations are y-x = 3 and 2(x + y) = 14


Solution:
In substitution method, we have a given equation of two variables, x and y.
First, divide in second equation by 2 in both sides.
x + y = 4 …. (1)
y – x = 3 => y = x + 3 ….(2)
Now, put the value of y in equation 1 and solve the equation for x, i.e
x + (x + 3) = 4
x + x + 3 = 4
2x = 4 –3
which gives x = 1/2.

Now, substitute x = 1/2 in any one of the given equation and find the value of y
y = 1/2 + 3
y = 7/2
Answer is : x = 1/2, y = 7/2

Substitution Method Algebra Watch Video

Solving Linear Equation by Substitution Method Algebra Watch Video

 

Q.
4x + 3y = 1 and x = 1 – y
Solution:
In substitution method, we have a given equation of two variables, x and y.
First you put the value of x in other given equation 4x = 2x + 3y and calculate the value of y.
Steps are:
x = 1 –y
Plug ‘x’ in first equation.
4(1 –y) + 3y = 1
Solve this equation for y
4 –4y + 3y = 1
4 –y = 1
y = 3
Substitute y = 1 in any one of the given equation and find the value of other variable
x = 1 –y
x = 1 –3 = –2
Answer is : x = –2, y = 3

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