Question

7у+2(х-3у)=5х-1 9х+3(х-2у)=2у-16

Answer 1

To solve this system of linear equations, we can follow these steps:

Equation 1: 7у + 2(х - 3у) = 5х - 1 Equation 2: 9х + 3(х - 2у) = 2у - 16

Let's start with Equation 1:

7у + 2(х - 3у) = 5х - 1 7у + 2х - 6у = 5х - 1 2х + (7у - 6у) = 5х - 1 2х + у = 5х - 1 у = 5х - 2х - 1 у = 3х - 1

Now let's substitute this value of у into Equation 2:

9х + 3(х - 2у) = 2у - 16 9х + 3(х - 2(3х - 1)) = 2(3х - 1) - 16 9х + 3(х - 6х + 2) = 6х - 2 - 16 9х + 3(-5х + 2) = 6х - 18 9х - 15х + 6 = 6х - 18 -6х + 6 = 6х - 18 -12х + 6 = -18 -12х = -24 х = 2

Now that we have the value of х, we can substitute it back into the equation for у:

у = 3х - 1 у = 3(2) - 1 у = 6 - 1 у = 5

So, the solution to the system of equations is х = 2 and у = 5.