Substitution Equation Two Variables

Determine if the system has one solution, infinitely many solutions, or no solution.

• One Solution

• Infinitely Many Solutions

• No Solution

0 = 0

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

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

• Run off the graph

• Don't touch

• Intersect

• Exist

Solve the system of equations.
y = 4x+1
3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

Solve for x and y.
y = 2/3x - 2
y = -x + 3

• (0,3)

• (0,-3)

• (3,0)

• (-3,0)

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

what is the first step in the substitution method?

• Step 2

• isolate one of the variables in one of the equations

• substitute in the value of the isolated variable into the other equation

Solve:
y = 2x -11
-3y = -6x -15

• (-1.5,-4)

• (1.5,4)

• No solution (parallel lines)

• Infinitely many solutions

Solve the system by using the substitution method

Solve the following systems of equations using substitution:

2y + x = -15

x = 3y

• (-3, -9)

• (-9, -3)

• (-3, 9)

• (9, -3)