Algebra

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Simultaneous Equations: Substitution

Another method of solving simultaneous equations involves substituting equations into one another.

Simultaneous equations allow us to find the points which two equations have in common. You might already be familiar with solving them through elimination, but substitution is another method of achieving the same result.

Simultaneous equations allow us to find:

We can solve simultaneous equations by substituting one equation into another.

For example, have a look at $y = 2x + 5$ and $x + y = 11$

Label the equations

$(1)\space y = 2x + 5$ and $(2) \space x + y = 11$

Replace $y$ in equation 2 by $2x+5$

$x + 2x + 5 = 11$

Solve $x + 2x + 5 = 11$ to find $x$

Substitute $x=2$ into $(1)\space y = 2x + 5$

$y = 2(2) + 5$

Solve $y = 2(2) + 5$ to find $y$

Good work!

$x=2$ and $y=9$

Try solving $y = x + 4$ and $x + y = 10$

Now try $y = x + 7$ and $x + y = 15$