Solve the following systems of the linear equation using any algebraic method. If possible check your solution.

Question

2x+5y=3

x-3y=7

Answer 1

From x-3y=7  we get  x=3y+7  by adding 3y to both sides of the equation.

 

Now plug this in for x in the first equation (2x+5y=3):

2(3y+7) + 5y = 3

 

Distribute the '2'

6y+14+5y = 3

 

Combine like terms, and subtract 14 from both sides to get:

11y = -11

 

Divide by 11:

y = -1

 

Now plug in -1 for y in either equation and solve for x:

x - 3(-1) = 7

 

-->  x + 3 = 7

-->  x = 4.

 

Final answer:  y = -1 and x = 4.

Answer 2

Multiply the second equation by -2 which yields

 

-2x + 6y = -14

 

now this can be called equation 3

 

Add equation 3 with equation 1 which yields 

 

2x + 5y = 3

-2x + 6y = -14

------------------

 

11y = - 11

 

y = - 1

 

Now substitute this value for y in eq 1

 

2x - 5 = 3

 

2x = 8

 

x = 8 / 2

 

x = 4

 

Now sub the values for x and y into eany of the 2 equations 

 

2(4) + 5(-1) = 3

 

So we know our answers are correct .