How to solve a system of equations with two unknown

The equation is an identity, where among the known members of one hides the number you want to put instead of the Latin letters, to the left and right sides came out of the same numeric expression. To find it, need to move in the same direction all known members in the other all unknown terms in the equation. How to solve a system of two such equations? Separate – can not be linked to a desired value from the system with each other. You can do this three ways: method substitution method addition method of graphing.

Instruction

1. Method of addition.
   You need to write two equations strictly under each other:
   
   2 –5Y=61
   
   -9x+5Y=-40.
   
   Next, fold each term of the equations, respectively, considering their signs:
   
   2+(-9x)=-7x, -5U+5U=0, 61+(-40)=21. As a rule, one of the sums containing the unknown amount, will be zero.
   Write the equation of the resulting members:
   
   -7x+0=21.
   The unknown: -7x=21, h=21:(-7)=-3.
   Already substitute the value found in any of the original equations and obtain a second unknown, solving a linear equation:
   
   2x–5Y=61, 2(-3)–5Y=61, -6-5Y=61, -5Y=61+6, -5Y=67, y=-13,4.
   The response of the system of equations: x=-3, y=-13,4.
2. The method of substitution.
   One equation should Express any of the required members:
   
   x–5Y=61
   
   -9x+4U=-7.
   
   x=61+5Y, x=61+5U.
   Substitute the resulting equation into the second instead of the number "x" (in this case):
   
   -9(61+5Y)+4U=-7.
   Then deciding
   
   the linear equation to find the number of "y":
   
   -549+45у+4U=-7, 45у+4U=549-7, 49у=542, y=542:49,≈11.
   In randomly selected (from the system) to insert the equation is already found "y" the number 11 and to compute the second unknown:
   
   X=61+5*11 x=61+55, x=116.
   Answer the given system of equations: x=116, y=11.
3. A graphical way.
   Is to practice finding the coordinates of a point which intersect the lines mathematically written in the system of equations. You should draw graphs of both direct separately in the same coordinate system. The General form of straight line equation: – y=KX+b. To build direct, it is sufficient to find the coordinates of the two points, and x is chosen arbitrarily.
   Given the system: 2x – y=4
   
   y=-3x+1.
   Video is based on the first equation, for convenience, it should be written: y=2x-4. To invent (easier) the values for x, substituting into equation, solving it, find y. You get two points, which is based on video. (see pic.)
   x 0 1
   
   at -4 -2
   Video is based on the second equation: y=-3x+1.
   To build a direct. (see pic.)
   
   x 0 2
   
   1 to 5
   Find the coordinates of the intersection point of two constructed lines on the chart (if the lines do not intersect, then the system of equations has no solution – it happens).