A system of linear equations is just a set of two or more linear equations.
In two variables (x and y), the graph of a system of two equations is a pair of lines in the plane.
There are three possibilities:
How to Solve a System Using The Substitution Method
Note: If it's easier, you can start by solving an equation for x in terms of y, also – same difference!
Solve the system
Solve the second equation for y.
y = 19 – 7x
Substitute 19 – 7x for y in the first equation and solve for x.
3x + 2(19 – 7x) = 16
3x + 38 – 14x = 16
–11x = –22
x = 2
Substitute 2 for x in y = 19 – 7x and solve for y.
y = 19 – 7(2)
y = 5The solution is (2, 5).
Note 2: If the lines are parallel, your x-terms will cancel in step 2, and you will get an impossible equation, something like 0 = 3.
Note 3: If the two equations represent the same line, everything will cancel in step 2, and you will get a redundant equation, 0 = 0.