x = 2
y = 2
see explanation below
Step-by-step explanation:
Using an example of system of equations:
x + y = 4
2x + y = 6
The equations are above are two systems of equations having two unknown x and y. There are different methods to solve the two equations. We can use elimination method or substitution method.
In elimination method, we eliminate one of the variables in order to get the other variable.
In substitution variable, we substitute for one of the variables in any of the equations.
Using elimination method to solve the two equations, the variable we want to eliminate must have the same coefficient.
Let's eliminate y. This is because the coefficient of y is the same in both equation.
The coefficient of y is 1.
Note: if we want to eliminate x, we will need the coefficent of both to be the same. One coefficent is 1, the order is 2.
This means we would multiply equation 1 by 2 and multiply equation 2 by 1. This will ensure they have same coefficient of 2.
x + y = 4 ...equation 1
2x + y = 6 ...equation 2
subtract equation 1 from 2:
2x - x + y - (+y) = 6 - 4
2x - x + y - y = 6 -4
x + 0 = 2
x = 2
We replace 2 with x in any of the equations in order to get y.
using equation 1: x + y = 4
2 + y = 4
y = 4 - 2
y = 2