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Solving Systems of Equations by Substitution a la Shmoop

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After leaving his day job as a substitute teacher… [Man walking through a school corridor]

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…Mister Uboat goes to his evening job as a substitute particle physicist. [Mr Uboat in a lab coat]

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Today's task at the lab is simple... solve for x and y to correctly align the particle [Two cannons labelled x and y shoot cannonballs]

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cannons.

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There are two equations, and x and y are the same value in each...

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two-x minus three-y equals negative-two...

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and...

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four-x plus y equals twenty-four. [Equations written on a blackboard]

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As a substitute, Mr. Uboat gets paid by the day, so he wants to get this done as efficiently [Flask bubbling]

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as possible.

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Let's solve this using, substitution.

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The second equation looks easier to solve, so we'll start with that one. [The second equation lights up]

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If we subtract four-x from both sides, we see that y equals twenty-four minus four-x.

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Now we'll just substitute y for 24 minus 4x into the first equation...

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to get two-x minus three, times open parenthesis, twenty-four minus four-x, closed parenthesis,

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equals negative two. [The working written out on a blackboard]

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Following the order of operations, we first distribute the minus 3 times the equation in the

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parentheses.

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Negative 3 times 24 equals 72, and negative 3 times negative 4x equals 12x, that's positive. [Finger pointing to the equation]

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When we write it all out we get two-x minus seventy-two plus twelve-x equals negative

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two.

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Combining the x's together on the left side, we get fourteen-x minus seventy-two equals [The x's are highlighted]

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negative-two.

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Add seventy-two to both sides, and see that fourteen-x equals seventy.

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Divide both sides by fourteen...and x equals five.

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Now, remember how y equals twenty-four minus four-x?

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Well, plug x as five into this equation to see what equals and you get twenty-four minus four times

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five.

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In other words, y equals twenty-four minus twenty, or y equals four. [Equation being solved on the blackboard]

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Our answer is five, four.

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Thanks to Mr. Uboat, the equation is solved!

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Now the particle cannons can collide particles in peace. [The cannons fire and an explosion follows, Mr Uboat emerges with a black face and frazzled hair]

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