Algebra one substitution
Introduction :
System of simultaneous equations can be solved by using substitution method.
Steps used to solve algebra one substitution method:
Step 1: Let us take any one of the equation from the given two equations. From this equation, write one variable in terms of the other variable.
Step 2: Next, substitute this in another one equation to get the single variable equation. Simplify and then find a one variable value.
Step 3: Substitute this variable value in any one of the equation, so we get the other another one variable value.
Now, we are going to see some of the problems on algebra 1 substitution.
Example problem for algebra one substitution :
Example problem 1:
Solve the following two equations by The Substitution Method:
3x + y = 4---------Equation (1)
x – y = 4---------Equation (2)
Solution:
Step 1: Let us consider the equation (1)
3x + y = 4
Subtract x on both sides of the equation
3x + y - 3x = 4 – 3x
y=-3x + 4------------------------Equation (3)
Step 2: Substitute this value of y in Equation (2). We get
x – y = 4
x – (-3x + 4) = 4
x + 3x – 4 =4
4x – 4 = 4
Add 4 on both sides of the equation
4x – 4 + 4 = 4 + 4
4x = 8
Divide by 4 on both sides of the equation
4x/4 = 8/4
x = 2
Step 3: Plugging this value of x in Equation (3), we get
y=-3x + 4
y=-6 + 4
y = -2
So, the solution of the simultaneous equations is x = 2 and y = -2.
One more example problem for algebra one substitution:
Solve the following two equations by substitution method:
y =5 x ------------Equation (1)
x + y = 12------------Equation (2)
Solution:
Step 1: Let us consider the equation (1)
y = 5x
Step 2: Substitute the value of y in Equation (2). We get
x + y = 12
x + (5x) = 12
x + 5x = 12
6x = 12
Divide by 6 on both sides of the equation
`(6x)/6` = `12/6`
x = 2
Step 3: Plugging this value of x in Equation (1), we get
y= 5x
y = 5(2)
y = 10
So, the solution of the simultaneous equations is (2, 10).
System of simultaneous equations can be solved by using substitution method.
Steps used to solve algebra one substitution method:
Step 1: Let us take any one of the equation from the given two equations. From this equation, write one variable in terms of the other variable.
Step 2: Next, substitute this in another one equation to get the single variable equation. Simplify and then find a one variable value.
Step 3: Substitute this variable value in any one of the equation, so we get the other another one variable value.
Now, we are going to see some of the problems on algebra 1 substitution.
Example problem for algebra one substitution :
Example problem 1:
Solve the following two equations by The Substitution Method:
3x + y = 4---------Equation (1)
x – y = 4---------Equation (2)
Solution:
Step 1: Let us consider the equation (1)
3x + y = 4
Subtract x on both sides of the equation
3x + y - 3x = 4 – 3x
y=-3x + 4------------------------Equation (3)
Step 2: Substitute this value of y in Equation (2). We get
x – y = 4
x – (-3x + 4) = 4
x + 3x – 4 =4
4x – 4 = 4
Add 4 on both sides of the equation
4x – 4 + 4 = 4 + 4
4x = 8
Divide by 4 on both sides of the equation
4x/4 = 8/4
x = 2
Step 3: Plugging this value of x in Equation (3), we get
y=-3x + 4
y=-6 + 4
y = -2
So, the solution of the simultaneous equations is x = 2 and y = -2.
One more example problem for algebra one substitution:
Solve the following two equations by substitution method:
y =5 x ------------Equation (1)
x + y = 12------------Equation (2)
Solution:
Step 1: Let us consider the equation (1)
y = 5x
Step 2: Substitute the value of y in Equation (2). We get
x + y = 12
x + (5x) = 12
x + 5x = 12
6x = 12
Divide by 6 on both sides of the equation
`(6x)/6` = `12/6`
x = 2
Step 3: Plugging this value of x in Equation (1), we get
y= 5x
y = 5(2)
y = 10
So, the solution of the simultaneous equations is (2, 10).