A way to solve a linear system algebraically is to use the substitution method. The substitution method functions by substituting the one y-value with the other.
(i) Find the value of one variable in terms of the other from one of the given equations.
(ii) Substitute the value of this variable in the other equation.
(iii) Solve the equation and get the value of one of the variables.
(iv) Substitute the value of this variable in any of the equation to get the value of other variables.
We're going to explain this by using an example.
We can substitute y in the second equation with the first equation since y = y.
This value of x can then be used to find y by substituting 1 with x e.g. in the first equation
The solution of the linear system is (1, 6).
The general method obtained for solving simultaneous equations as follows:
1. To express y in terms of x from any one of the equations.
2. To substitute this value of y in the other equation.
3. One value of x will be obtained, by solving the equation in x thus obtained.
4. Substituting this value of x in any of the equations, we will get the corresponding value of y.
5. The solution of the two given simultaneous equations will be given by this pair of values of x and y.
6. Similarly expressing x in terms of y from an equation and substituting in the other, we can find the value of y. Putting this value of y in any one of the equations, we can find the value of x and thus we can solve the two linear simultaneous equations.