Solve the systems of equations algebraically. 3x + y = -5; x + 4y = 2

The solution for system of equations 3x + y = -5; x + 4y = 2 is x = -2 and y = 1

Solution:

With the help of substitution method of algebraic equations,

3x + y = - 5 equation 1

x + 4y = 2 equation 2

Multiplying equation 1 by 4, equation 1 can be rewritten as  

12x + 4y = -20 equation 3

Multiplying equation 2 by -1, equation 2 can be rewritten as,

- x - 4y = -2 equation 4

Solving equation 3 and 4, we get

12x + 4y = -20

-x - 4y = -2

11x = -22

x = -2

Substitute x = -2 in equation 2

-2 + 4y = 2

4y = 4

y = 1

hence we obtain x = -2 and y = 1