Question

-x+y=4 4x+y=-1 математика

Answer 1

{-x+y=4
{ 4x+y=-1
{y=4+x
{4x+4+x=-1
 
{y=4+x
{5x=-1-4
{y=4+x
{5x=-5
 
{y=4+x
{x=-1
 
{y=4-1
{x=-1
 
{y=3
{x=-1
 
Ответ: (-1;3)

Answer 2

To solve the system of equations -x + y = 4 and 4x + y = -1, we can use either the substitution method or the elimination method. Let's use the elimination method:

Step 1: Add the equations to eliminate one variable. (-x + y) + (4x + y) = 4 + (-1)

Step 2: Simplify the equation. 3x + 2y = 3

Now, we have one equation with two variables. To find the values of x and y, we need another equation. We can use the first equation -x + y = 4:

Step 3: Solve for y in terms of x from the first equation. y = x + 4

Step 4: Substitute y = x + 4 into the equation from Step 2. 3x + 2(x + 4) = 3

Step 5: Solve for x: 3x + 2x + 8 = 3 5x + 8 = 3 5x = 3 - 8 5x = -5 x = -5/5 x = -1

Step 6: Substitute the value of x back into the first equation to solve for y: -y + y = 4 0 = 4

The equation 0 = 4 is not possible, which means there is no solution to the system of equations. In other words, the two lines represented by the equations are parallel and do not intersect, hence no common point (x, y) satisfies both equations simultaneously.