Mathspics: Linear equation of two variables

Monday 18 April 2016

Linear equation of two variables

A linear system of two equations with two variables is any system that can be written in the form.
ax + by =p
cx + dy =q

where any of the constants can be zero with the exception that each equation must have at least one variable in it.

Also, the system is called linear if the variables are only to the first power, are only in the numerator and there are no products of variables in any of the equations.

Here is an example of a system with numbers.
3x - y=7 ................(a)
2x+2y=3 .................(b)
now (a) x 2 + (b)

6x - 2y =14
2x + 2y =3
___________
8x =17 because 2y to 2y is cencle
therefore x=17/8
put this value in (a)
3 *17/8 -y =7
=> 51/8 - 7 =y
=> 51-56/8 =y
=> -5/8 = y

Before we discuss how to solve systems we should first talk about just what a solution to a system of equations is. A solution to a system of equations is a value of x and a value of y that, when substituted into the equations, satisfies both equations at the same time.

Solve each of the following systems of equations

(a) x+y=1 ...................1

2x+y=2 ..................2

solve->

for solve this equation , we can subtract it from 2 to 1

so we can find

2x+y=2

x+y=1

- - = -

________

x=1

put x=1 in equation (1)