Intro to Systems of Equations Substitution

Why might we use substitution to solve instead of solving by graphing?

• We can find fractional answers more easily

• We don't need graph paper or a graphing calculator

• One or both of the equations aren't in slope-intercept form

• We find substitution to be an easier method

Answer explanation

Any of these reasons are valid!

What does it mean to substitute?

• To guess and check

• To graph and find the intersection point

• To replace the value of a variable with an equivalent expression

• To add different variables together and see what you get

Which shows correct substitution for the system:

Answer explanation

Notice that when we substitute, we should no longer have two different variables (instead of y and x, we just have x)

Which shows correct substitution for the system:

Answer explanation

Notice that we replaced y with an equivalent expression in the correct option

The solution to a system of equations is any ordered pair that makes both equations true. 

• TRUE

• FALSE

^{What is the solution?} 

• 1

• -2

• (1, 2)

• (1, -1)

You can solve systems using these methods:

• graphing, substitution, and elimination

• rearranging, thinking, and guessing

• only by graphing

• only by elimination

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph

• Don't touch

• Intersect

• Exist

What point is the solution to these two equations?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Find the solution to the system.
y = x-6
y = -3x + 2

• (0, -6)

• (6, 0)

• (-4, 2)

• (2, -4)