Solving Systems of Linear Equations by Graphing and Substitution

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

• Run off the graph

• Don't touch

• Intersect

• Exist

y = -3x + 11

5x + y = 21

• (1, -5)

• (1, 5)

• (-4, 5)

• (5, -4)

x - 3y = -13

4x + 2y = 4

• (1, 4)

• (-1, -4)

• (-1, 4)

• (1, -4)

−3x − 3y = 3
y = −5x − 17 

• (-4,3)

• (4,-3)

• (3,-4)

• (-3,-4)

y = 4x - 2 y = -x + 3

• (-2,-1)

• (-1,-2)

• (1,2)

• (2,1)

How many Solutions?

• One Solution

• No solution

• Infinitely Many Solutions

• (0, -1)

If the solution is infinitely many the lines will ________?

• intersect at exactly one point

• be parallel

• overlap each other

• never exist

-5x - 4y = -9

y = 6

• (3, 6)

• (6, -3)

• (-3, 6)

• (6.8, 3)

In 3x + 2y = 10 and x - 5y = 18, which variable should you isolate first?

• The x in the first equation

• The y in the first equation

• The x in the first equation

• The x in the second equation

y = 2x + 5

2x + 2y = 4

• (1, 7)

• (7, 1)

• (2, 9)

• (-1, 3)