-8x-5y=10 5x-15y=30 solve by elimination

Question

solve by elimination

Answer 1

Solve by elimination

-8x - 5y = 10

5x - 15y = 30

• First choose which variable to eliminate; let's eliminate y
• To do this the y term in the top equation added to the y term in the bottom equation must equal zero. This is called the additive inverse.
• We can do this by multiplying the entire top equation by -3

-3(-8x - 5y = 10)

24x + 15y = -30

• Now we can combine the two equations

24x + 15y = -30

  5x  - 15y =  30

29x   + 0y =   0

• Then divide both sides by 29 to solve for x

29x/29 = 0/29

x = 0

• Next we can substitute our x value into the top equation to solve for y

-8x - 5y = 10

-8(0) - 5y = 10

0 - 5y = 10

• Divide both sides by -5 to isolate y

-5y/-5 = 10/-5

y = -2

• Now we should check our answer with the second equation.

5x - 15y = 30

5(0) - 15(-2) = 30

0 + 30 = 30

30 = 30 √

 

 

x = 0   y = -2

Answer 2

-8x - 5y = 10     I.

5x-15y=30         II.

 

Multiply Equation I. by (-3)

 

24x + 15y = -30     I.'

-5x - 15y = 30

 

Add the two Equations together:

 

x[24 +(-5)] = 0

 

19x = 0

 

∴ x = 0

 

If x = 0, then, by Equation I.

 

-5y = 10

 

y = -2

 

Solution: (0,2)

 

HINT: You can also graph the two lines and find that they intersect each other at (0,2)