solve the top equation for x in terms of y: y= x-5Now substitute this expression for x into the bottom equation:2x-3(x-5)= 13Solve for x then plug it in to get y.Same concept for three variables.......
2*x - 3*y = 4
-2*x +4*y =6
ADD both equations:
2*x - 3*y = 4
y =10
(we already know, that x = 17, so the solution is {x = 17, y = 10}, but I keep going for sake of illustration)
Multiply second by 3 and ADD to the first:
2*x = 34
3y = 30
Multiply first by 1/2 and second by 1/3:
x = 17
y = 10
You may solve any system of any order in this way. It's all linear, therefore you can multiply with factor and add as you like - just think of how to eliminate the unknowns in a diagonal fashion, as shown.
To solve a system of three equations in the three variables x, y, z, you need to find the assignment of numbers to the variables such that all the equations are satisfied.
The simplest kind of linear system involves two equations and two variables:
X+Y=5
2X+3Y= 13
One method for solving such a system is as follows. First, solve the top equation for x in terms of y:
y= x-5
Now substitute this expression for x into the bottom equation:
2x-3(x-5)= 13
Solve for x then plug it in to get y.
Same concept for three variables.
