The equation is an identity where among the famous members one number which needs to be put instead of a Latin letter in order that from the left and right side the identical numerical expression turned out disappears. That to find it, it is necessary to transfer to one party everything the famous members, to another - all unknown members of the equation. And how to solve a system from two such equations? Separately – it is impossible, it is necessary to connect required sizes from a system with each other. It is possible to make it in three ways: by a substitution method, by method of addition and by method of creation of schedules.
Instruction
1. Way of addition. It is necessary to write down two equations strictly the friend under the friend: 2 – 5u =61-9kh +5u =-40. Further to put everyone composed the equations respectively, considering their signs: the 2nd + (-9h)=-7kh, - 5u +5u =0, 61+(-40)=21. As a rule, one of the sums containing unknown size will be equal to zero. To work out the equation from the received members: - the 7th +0=21. To find unknown: - the 7th =21:(-7). To substitute Part =21 already found value in any of the initial equations and to receive the second unknown, having solved the linear equation: to a 2kh-5 of =61, 2 (-3)-5y=61, - the 6-5th =61, - 5u =61+6, - 5u =67, at =-13.4. Answer of a system of the equations: x =-3, at =-13.4.
2. Way of substitution. From one equation it is necessary to express any of required members: x-5u =61-9kh +4u =-7.h =61+5u, x =61+5u. To substitute the turned-out equation in the second instead of number "X" (in this case):-9 (61+5u) +4u =-7. Further the reshivlineyny equation to find number "Y": - 549+45u +4u =-7, 45u +4u =549-7, 49u =542, at =542:49, u11. In randomly chosen (from a system) the equation to insert number 11 instead of already found "Y" and to calculate the second unknown: X =61+5*11, x =61+55, x =116. Answer of this system of the equations: x =116, at =11.
3. Graphic way. Consists in practical finding of coordinate of a point in which the straight lines which mathematically are written down in the system of the equations are crossed. It is necessary to draw schedules of both straight lines separately in one system of coordinates. General view of the equation of a straight line: – at =kkh +b. To construct a straight line, it is enough to find coordinates of two points, and, x is chosen randomly. Let the system be given: the 2nd – at =4 at =-3h +1. The straight line on the first equation is under construction, for convenience it needs to be written down: at =2kh-4. It is (easier) to think up values for X, substituting it in the equation, having solved it, to find Y. Two points on which the straight line is under construction turn out. (fig. cm) x 0 1u-4 - 2stroitsya a straight line on the second equation: at =-3h +1. Also to construct a straight line. (fig. cm) x 2u 1 - 5nayti coordinates of a point of intersection of two constructed straight lines on graphics (if straight lines are not crossed, then the system of the equations has no decision – so is 0).