Solving Systems of Linear Equations

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)

Parallel Lines never intersect because...

• they have the same slopes. 
• they have the same y-intercept.
• they have different slopes.
• they have different y-intercepts. 

This system has _____ solutions

• 0
• 1
• 2
• Infinitely many

You can solve systems using these methods:

• graphing, substitution, and elimination

• rearranging, thinking, and guessing

• only by graphing

Solve this system by substitution.

• (1, -4)

• (1, 4)

• (-4, -7)

• (-7, -4)

What variable do you eliminate, and what do you multiply the equation(s) by?

5x + y = 9

10x − 7y = −18

• You eliminate x, and multiply the top equation by 11

• You eliminate y, and multiply the top equation by 7

Solve the system given:
3x - y = 7
2x + y = 3

• (-1,2)
• (5,4)
• (4,5)
• (2,-1)

Solve using elimination. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 
• Infinite number of solutions  
• (−6, 10) 
• (6, 4) 

Solve using elimination.
-4x - 6y = 6
4x + 6y = -4

• no solution
• (2,0)
• (-4,0)
• (0,0)