Simultaneous equations by substitution:

Solve the subsequent simultaneous equations by substitution.

3x + 4y = 6      5x + 3y = -1

Solution:

Solve for x:

3x = 6 - 4y

x = 2- 4y /3

Substitute the value for x within the other equation:

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

10 - 20y/3 +3y = -1

 10- 20y/3 +9y/3 = -1

10-11y/3 = -1

-11y/3 = -11

y = 3

Substitute y = 3 into the first equation:

3x + 4(3) = 6

3x = -6

x = -2

Check the solution through substituting x = -2 and y = 3 into the original equations.

3x +4y = 6                   5x + 3y = -1

3(-2) +4(3) = 6            5(-2) + 3(3) = -1

-6 +12 = 6                   -10 + 9 = -1

6= 6                             -1 = -1

Therefore, the solution checks.