Х+2у=0 х+у-2х+7у=8
To solve the system of equations:
- х + 2у = 0
- х + у - 2х + 7у = 8
We can start by eliminating one of the variables. Let's eliminate х.
Multiply equation 1 by -1: -1(х + 2у) = -1(0) -х - 2у = 0
Now we have two equations: -х - 2у = 0 х + у - 2х + 7у = 8
Combine the х terms in the second equation (-х and -2х) to get: -х + у - 2х + 7у = 8 -3х + 8у = 8
We can solve these two equations together. Let's multiply the first equation by 3 to match the coefficients of the х terms: -3(х + 2у) = -3(0) -3х - 6у = 0
Now we have two new equations: -3х - 6у = 0 -3х + 8у = 8
We can subtract the first equation from the second equation: (-3х + 8у) - (-3х - 6у) = 8 - 0 -3х + 8у + 3х + 6у = 8 14у = 8 у = 8/14 у = 4/7
Now substitute the value of у back into one of the original equations, let's use equation 1: х + 2(4/7) = 0 х + 8/7 = 0 х = -8/7
Therefore, the solution to the system of equations is: х = -8/7 у = 4/7
