Question

Решить систему уравнений:

Answer 1

{4p+3q=-12
{p-4q=-41

{p=-41+4p
{4*(-41+4q)+3q=-12

{p=-41+4p
{-164+16q+3q=-12

{p=-41+4p
{19q=152

{p=-41+4p
{q=8

{p=-41+4*8
{q=8

{p=-9
{q=8

Answer 2

Solving the System of Equations

To solve the system of equations, we will use the given equations and apply algebraic methods to find the values of x and y.

The system of equations is as follows:

Equation 1: x - 5xy + 4y = 0 Equation 2: 2x - y = 31

To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution.

Method of Substitution

Step 1: Solve Equation 2 for x in terms of y: From Equation 2, we have: 2x - y = 31 2x = y + 31 x = (y + 31)/2

Step 2: Substitute the value of x in Equation 1: x - 5xy + 4y = 0 ((y + 31)/2) - 5((y + 31)/2)y + 4y = 0

Simplifying the equation: (y + 31)/2 - 5(y + 31)/2 * y + 4y = 0 (y + 31 - 5(y + 31)y + 8y)/2 = 0 (y + 31 - 5y - 155y + 8y)/2 = 0 (y - 155y + 8y + 31 - 5y)/2 = 0 (-155y + 4y + 31)/2 = 0 (-151y + 31)/2 = 0

Step 3: Solve for y: -151y + 31 = 0 -151y = -31 y = -31/-151 y = 31/151

Step 4: Substitute the value of y back into Equation 2 to find x: 2x - y = 31 2x - (31/151) = 31 2x = 31 + (31/151) 2x = (31*151 + 31)/151 2x = (4681 + 31)/151 2x = 4712/151 x = (4712/151)/2 x = 4712/302 x = 78/151

Therefore, the solution to the system of equations is: x = 78/151 y = 31/151

The solution can also be written as a coordinate point: (78/151, 31/151).

Answer

The solution to the system of equations is x = 78/151 and y = 31/151.