When solving a system of equations by elimination, we should first analyze the to decide which variable to eliminate. One of the variables must have the same coefficient in both equations, disregarding their signs. In the system
there is no such variable. Therefore, we now have to manipulate the equations so that this condition is met. This is done by multiplying either one or both equations by some number. Notice that if we multiply the first equation by 3,
the coefficients of y
will be 3
Therefore, we'll choose to eliminate the variable y.
Since the coefficients of y have different signs, the variable will be eliminated by adding the two equations.
The resulting equation is 3x=6.
Solving this equation gives the x
-coordinate of the solution to the system.
To find the corresponding y
-coordinate, we substitute x=2
into either original equation. For simplicity, let's choose -2x+y=4.
The solution to the system is the point (2,8).