Lesson Systems Substitution

There are several ways to solve systems of equations

Graphing

There are several ways to solve systems of equations

Graphing

Substitution

There are several ways to solve systems of equations

Graphing

Substitution

Elimination

There are several ways to solve systems of equations

This lesson will deal with substitution

Graphing

Substitution

Elimination

When given a system of equations

y = 2x - 5

x + y = 4

When given a system of equations

You can solve for x and y by substituting

y = 2x - 5

x + y = 4

When given a system of equations

You can solve for x and y by substituting

Notice the second equation

y = 2x - 5

x + y = 4

When given a system of equations

You can solve for x and y by substituting

Notice the second equation

y = 2x - 5

x + y = 4

second equation

When given a system of equations

You can solve for x and y by substituting

Notice the second equation

The y is by itself

y = 2x - 5

x + y = 4

When given a system of equations

You can solve for x and y by substituting

Notice the second equation

The y is by itself

y = 2x - 5

x + y = 4

y by itself

When given a system of equations

You can solve for x and y by substituting

Notice the second equation

The y is by itself

That means 2x - 5 is the exact same as y

y = 2x - 5

x + y = 4

2x - 5

When given a system of equations

You can solve for x and y by substituting

Notice the second equation

The y is by itself

That means 2x - 5 is the exact same as y

So we can substitue a 2x - 5 anywhere we see a y

y = 2x - 5

x + y = 4

Fill in the blank

We see a y in the first equation

y = 2x - 5

x + y = 4

We see a y in the first equation

y = 2x - 5

x + y = 4

a 'y'

We see a y in the first equation

so we can replace that y with a 2x - 5

y = 2x - 5

x + y = 4

a 'y'

We see a y in the first equation

so we can replace that y with a 2x - 5

y = 2x - 5

x + (2x - 5) = 4

put a 2x - 5 in for y

What can we put for y?

We see a y in the first equation

so we can replace that y with a 2x - 5

and we can solve our new equation

y = 2x - 5

x + (2x - 5) = 4

We see a y in the first equation

so we can replace that y with a 2x - 5

and we can solve our new equation

y = 2x - 5

x + (2x - 5) = 4

new equation

We see a y in the first equation

so we can replace that y with a 2x - 5

and we can solve our new equation

y = 2x - 5

x + (2x - 5) = 4

new equation

x + (2x - 5) = 4

We see a y in the first equation

so we can replace that y with a 2x - 5

and we can solve our new equation

y = 2x - 5

x + (2x - 5) = 4

new equation

x + (2x - 5) = 4

x + 2x - 5 = 4

We see a y in the first equation

so we can replace that y with a 2x - 5

and we can solve our new equation

y = 2x - 5

x + (2x - 5) = 4

new equation

x + (2x - 5) = 4

x + 2x - 5 = 4

3x - 5 = 4

We see a y in the first equation

so we can replace that y with a 2x - 5

and we can solve our new equation

y = 2x - 5

x + (2x - 5) = 4

new equation

x + (2x - 5) = 4

x + 2x - 5 = 4

3x - 5 = 4

3x = 9

We see a y in the first equation

so we can replace that y with a 2x - 5

and we can solve our new equation

y = 2x - 5

x + (2x - 5) = 4

new equation

x + (2x - 5) = 4

x + 2x - 5 = 4

Find the value for x

3x - 5 = 4

3x = 9

x = 3

So now we know x is 3

y = 2x - 5

x + y = 4

x = 3

So now we know x is 3

But we have to find y

y = 2x - 5

x + y = 4

x = 3

So now we know x is 3

But we have to find y

y = 2x - 5

x + y = 4

x = 3

y = ?

So now we know x is 3

But we have to find y

We do that by putting 3 in for x

y = 2x - 5

x + y = 4

x = 3

y = ?

So now we know x is 3

But we have to find y

We do that by putting 3 in for x

Let's use the second equation (we can use either)

y = 2x - 5

x + y = 4

x = 3

y = ?

So now we know x is 3

But we have to find y

We do that by putting 3 in for x

Let's use the second equation (we can use either)

y = 2(3) - 5

x + y = 4

put 3 in for x

What do you put in for x?

x = 3

y = ?

So now we know x is 3

But we have to find y

We do that by putting 3 in for x

Let's use the second equation (we can use either)

y = 2(3) - 5 = 1

x + y = 4

and solve

x = 3

y = ?

So now we know x is 3

But we have to find y

We do that by putting 3 in for x

So we know that y = 1

Let's use the second equation (we can use either)

y = 2(3) - 5 = 1

x + y = 4

and solve

x = 3

y = ?

So now we know x is 3

But we have to find y

We do that by putting 3 in for x

So we know that y = 1

Let's use the second equation (we can use either)

y = 2(3) - 5 = 1

x + y = 4

and solve

What does y equal?

x = 3

y = 1

so that's our answer

y = 2x - 5

x + y = 4

x = 3

y = 1

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