Solving Systems of Equations Linear

What is the definition of 'no solution'?

• When the graphs of two linear equations overlap and intersect at infinitely many points

• When a system of two equations has graphs that never intersect because lines are parallel

• To replace a variable with a number or another expression in an algebraic expression

• Algebraic process of eliminating a variable in a system of equations by combining the equations through addition

What does it mean when a system of linear equations has no solution?

• The graphs of the equations intersect at a single point

• The graphs of the equations are parallel and do not intersect

• The graphs of the equations coincide, meaning they are the same line

• The graphs of the equations intersect at infinitely many points

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

• TRUE

• FALSE

You can solve systems using these methods:

• graphing, substitution, and elimination

• rearranging, thinking, and guessing

• only by graphing

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 given:
3x - y = 7
2x + y = 3

• (-1,2)

• (5,4)

• (4,5)

• (2,-1)

-4x - 6y = 6
4x + 6y = -4

• no solution

• (2,0)

• (-4,0)

• (0,0)

This system has _____ solutions

• 0

• 1

• 2

• Infinitely many

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

Solve this system by substitution.

• (1, -4)

• (1, 4)

• (-4, -7)

• (-7, -4)