Question

|x - 1| + y = 4, x + y = 3;

Answer 1

Ответ:

|x-1|+y=4

|x-1|+0=4

|x-1|=4

x-1=4

x-1=-4

x+y=3

x+y-3=3-3

x+y-3=0

Answer 2

To solve the system of equations:

1. |x - 1| + y = 4
2. x + y = 3

You can approach this problem by considering two cases for the absolute value expression |x - 1|:

Case 1: x - 1 is positive or zero: In this case, the absolute value expression |x - 1| is the same as x - 1. So, we have:

x - 1 + y = 4 (from equation 1) x + y = 3 (from equation 2)

Now, you can solve this system of linear equations by either substitution or elimination. We'll use the elimination method here. Subtract equation 2 from equation 1 to eliminate y:

(x - 1 + y) - (x + y) = 4 - 3

This simplifies to:

x - 1 - x - y + y = 1

The x terms cancel out, and you're left with:

-1 = 1

However, this equation is not true, so this case does not yield a valid solution.

Case 2: x - 1 is negative: In this case, the absolute value expression |x - 1| becomes -(x - 1) or -x + 1. So, we have:

-x + 1 + y = 4 (from equation 1) x + y = 3 (from equation 2)

Now, we can use the elimination method again. Add equation 2 to equation 1 to eliminate y:

(-x + 1 + y) + (x + y) = 4 + 3

This simplifies to:

1 + 2y = 7

Subtract 1 from both sides:

2y = 7 - 1 2y = 6

Now, divide both sides by 2 to solve for y:

2y/2 = 6/2 y = 3

Now that you have the value of y, you can substitute it back into equation 2 to find the value of x:

x + 3 = 3

Subtract 3 from both sides:

x = 0

So, the solution to the system of equations is:

x = 0 y = 3