Linear Equations

Question

1. Solve the following system of linear equations:
x+2y=4

6x+15y=33

 

2. Solve the following system of linear equations:

x-2y=2

5x-10y=10

Solve for y in terms of x

 

 

 

Answer 1

just use the first equation in (1) to solve for y, and substitute that into the second equation.

 

In the second system, OBSERVE that the first equation, when multiplied by 5, gives you the second equation. therefore this system is DEPENDENT (equivalent to just having ONE equation) so the solution is the entire line represented by x-2y = 2. Since a line has infinitely many points, there are infinitely many solution points!

Answer 2

First problem:

 

(i)   x + 2y = 4
(ii)  6x + 15y = 33

 

From (i) get

 

x = 4 - 2y 

 

Plug this into (ii) and get

 

6(4 - 2y) + 15y = 33

 

Solve for y.

 

24 - 12y + 15y = 33

24 + 3y = 33

y = (33 - 24)/3 = 9/3 = 3

 

y = 3

 

x = 4 - 2y = 4 - 2(3) = -2

 

x = -2

 

Second problem:

 

x - 2y = 2
5x - 10y = 10

 

Note that if you divide by 5 on both sides of the second equation, you get

 

x - 2y = 2,

 

which is the same as the first equation.  The two lines are the same.