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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.
(x+y+1)dy/dx=1
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