Systems of Equations by Graphing and Substitution

Lesly graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-3,-8)

• (-8,-3)

• (3,-8)

• (8,3)

Solve for x and y
5x + 3y = 7
y = 4

• (4,1)

• (4,-1)

• (1,4)

• (-1,4)

Solve for x and y
2x − 3y = −1
 y = x − 1

• (-2,-3)

• (0,-1)

• (3,4)

• (4,3)

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

If a system of equations has infinitely many solutions, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• the same line (coinciding lines)

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• the same line (coinciding lines)

Is (1,10) a solution to

y=7x+5

y=x+9

• yes

• no

Is (1,7) a solution for

y=3x+4

y=x+6

• yes

• no

Is (4,9) a solution for

y=x+5

y=2x+1

• yes

• no

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

• Run off the graph

• Don't touch

• Intersect

• Exist