SLE - Solve Systems of Equations Using Substitution (Lesson)

Solve Systems of Equations Using Substitution

Another way to solve a system of equations is by using substitution. When you substitute, you isolate one variable in one of your equations, then substitute that into the other equation. This gives you an equation in one variable - which you know how to solve!

Let's look at an example:

2x - 3y = -2

4x + y = 24

First, let's isolate one of the variables - since the y in the second equation has a coefficient of 1, it would be the easiest to isolate.

Change 4x + y = 24 to y = -4x + 24

Now substitute that into the other equation for y, then solve for x.

2x - 3(-4x + 24) = -2

2x + 12x - 72 = -2

14x - 72 = -2

14x = 70

x = 5

Once you solve for one of the variables, substitute it in to find the other variable (you can use either equation):

2(5) - 3y = -2

10 - 3y = -2

-3y = -12

y = 4

So, the solution to this system of equations is (5, 4)!

Watch this video to see a few more examples:

Solving Systems of Equations Using Substitution Practice

Solve these systems of equations using substitution:

y = 6x - 11 and -2x - 3y = -7
-3x + 3y = 4 and -x + y = 3
-7x - 2y = -13 and x - 2y = 11
2x + 5y = 2 and -4x - 10y = -4

Bob's Busy Taxi charges a $5 initial fee and $0.25 a mile. Larry's Taxi Cab charges a $2 initial fee and $0.40 a mile.

a. Write a function for Bob's Busy Taxi.

b. Write a function for Larry's Taxi Cab.

c. At what mileage would the charge be the same for the two companies?

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