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Want to watch animated videos and solve interactive exercises about solving systems of equations using the substitution method?
Click here to try the Video Crash Course called “Systems of Equations”!
The substitution method is my favorite way to solve systems of equations. It will always work—it is actually quite mechanical. The answer will always appear, as long as you follow the recipe. It’s an advantage to set up the equations in separate columns when you use the substitution method.
Rule
Example 1
Solve this system of equations with the substitution method:
Example 2
Mom, Aunt Beth, and the three kids are looking forward to watching the world champion Magnus Carlsen play in a chess tournament in London. They have to pay in total for their tickets.
David Beckham also wants to watch the same chess tournament. He and his wife Victoria will be joined by one of David’s buddies, and his oldest son. They pay a total of for their tickets. Find the price of an adult ticket and a child ticket.
The unknowns in this system is the price of an adult ticket and the price of a child ticket. Let’s call the adult ticket and the child ticket .
The equation describing the situation of Mom, Aunt Beth, and the three kids looks like this:
(3) |
The equation for David Beckham and his companions looks like this:
(4) |
You choose to start with Equation (4), because that equation has a variable that stands on its own, .
Apply this expression to Equation (3) and solve for :
Surprisingly, the adult tickets are actually cheaper than the child tickets. Adult tickets cost £ and child tickets cost £.