The Substitution Method

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The Substitution Method A method to solve a
system of linear equations in 2 variables
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When you Solve a system of equations you are
looking for a solution that will solve every
equation in the system (group).
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???A linear equationAx By Chas an infinite
number of solution????
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How do we start with two equations , each having
an infinite number solutions, and find the common
solution (if any)???
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This Method will create one combined equation
with only one variable. This is the kind of
equation that you can solve!
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Substitution Method - Step One
Choose either equation and solve for either
variable.
(Choose the easiest one the solve. )
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2x y 53
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x 5y 139
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Choose either equation and solve for either
variable.
(Choose the easiest one the solve. )
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In this problem you could have solved equation 1
for y or solved equation 2 for x.
y -2x 53
x - 5y 139
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Substitution Method - Step Two
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If you solve for y in the first equation take
this expression and substitute it in for y in the
2nd equation
y -2x 53
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This will create one combined equation with only
one variable. This is the kind of equation that
you can solve!
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2x y 53
y -2x 53
Now solve for x
x 5y 139
x 5 (-2x 53) 139
joined
x -10x265 139
-9x 265 139
-9x -126
x -126/-914
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After solving the combined equation .
(Substitute the value you found in step 2 to back
into the equation)
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y -2x 53
Substitute the value you found for the first
variable back into one of the original equations
From the last step you found that x was 14.
Take this value and plug it back into one of the
original equations and find y.
y -2x 53
y -2(14)53
(x , y ) (14,25)
y -285325
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x 4y 5
x - 4y 5
3x 2y 113
3 (4y 5) 2y 113
3 ( ) 2y 113
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Im thinking of two numbers. One number is one
less then twice the other. The difference of the
numbers is 18. Find the numbers.
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Im thinking of two numbers. One number is one
less then twice the other. The difference of the
numbers is 18. Find the numbers.
Let x and y represent the numbers. Write two
equations to represent the relationships.
y-x18
y2x-1
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y 2x - 1
y 2x-1
y - x 18
2x - 1 - x 18
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John had all dimes and quarters worth 5.45 If he
had 35 coins in all, find out how many of each
coin he had.
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John had all dimes and quarters worth 5.45 If he
had 35 coins in all, find out how many of each
coin he had.
Let d the of dimes and q the of
quarters Write two equations.
dq35
10d25q545
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q 35 - d
d q 35
10d 25q 545
10d 25(35 - d) 545
q 35 - d
q 35 - 22
q 13
Substitute the value you found for the first
variable back into one of the original equations
of dimes 22 of quarters 13