Exploring the Substitution Method in Systems of Equations

The video tutorial explains how to solve a system of equations using the substitution method. It begins by introducing the concept of substitution and demonstrates how to substitute one variable with an expression to solve for the other variable. The tutorial provides a step-by-step guide on substituting y-4 for x and solving for y, followed by verifying the solution. It then shows an alternative approach by substituting x+4 for y and solving for x, confirming that both methods yield the same solution.

When solving using substitution we want to create

• Solve for both variables simultaneously

• 1 equation with 1 variable that we can solve for

• Both variables to equal the same number

• Graph both equations

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

The 2nd equation tells us that x =

• y - 4

• x + 7

• 2y - 7

• y

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

If x = y -4, then in the first equation what can I substitute for x (replace x with)

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

The top equation becomes 2 y =

If I combine my like terms on the right (the constants) I get

If I then subtract y from each side the result is

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CCSS.6.EE.B.7

Since we know that x = y - 4, we substitute in y = 3 and get the equation

Simplifying we get a solution for x

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CCSS.8.EE.C.7B

Putting the solution into a coordinate point (x, y) you get

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

After substituting x with y - 4, what is the next step?

• Graph the equation

• Solve for x

• Solve for y

• Substitute y with x + 4