Linear equations (two variables)

Solve the system by elimination.  

−8x − 10y = 20
−8x − 6y = −4 

• Infinite number of solutions  
• (6, 5) 
• (−6, −5) 
• (5, −6) 

( 2x - y = 4 , 6x - 3y = 12 ) How many solutions do you think are in this equation?

• No solutions

• Infinite solutions

• One solution

Solve the system of equations and determine what type of solution does it have. 
 $y=-6x+1$  
 $12x+2y=2$  

• Infinitely Many Solutions

• No Solution

The value of s for which sx +2y =5 and 3x+ y =1  have unique solution, is:

• s equal to 1

• s not equal to 6

• s equal to 6

• s equal to 2

in a system of linear equations this means that the lines are the same and all ordered pairs will make both equations true.

• infinite solutions

• collinear

• slope

• y-intercept

How many solutions would the following system have?

2y+x=4

2y=-x+4

(Hint: Rearrange one of the equations)

• Infinite solutions.

• No solutions.

• One solution.

• Infinitely Many Solutions

• (0, 5)

• No Solution

• (-5, 0)

• Infinitely Many Solutions

• No Solution

• (0, 2)

• (-1, 9)

Given the linear equation 12x - 4y = 20, which of the following linear equations in two variables is such that the geometrical representation of the pair formed is two intersecting lines. 1. 6x + 4y =10 2. 6x - 2y = 10

• 1

• 2

• 1 and 2 both

• Neither

Answer explanation

Equation is 12x - 4y =20 If the other line has to be intersecting then a₁/a₂ ≠ b₁/b₂ For equation 1, a₁/a₂ = 12/6 = 2 b₁/b₂ = -4/4 = - 1 Therefore, equation 1 and given equation form an intersecting pair of lines. For equation 2, a₁/a₂ = 12/6 = 2 b₁/b₂ = -4/-2 = 2 since a₁/a₂ = b₁/b₂ , equation 2 and given equation do not form an intersecting pair of lines So correct option is option 1.