{х+у=10 (100х+70у+у+7х-у=259

To solve this system of equations, we will use the method of elimination.

Given equations:

1. x + y = 10
2. 100x + 70y + y + 7x - y = 259

First, let's simplify equation 2:

2. 100x + 7x + 70y + y - y = 259 107x + 70y = 259

Now, let's multiply equation 1 by 70 to make the coefficient of y the same as in equation 2:

1. 70(x + y) = 70(10) 70x + 70y = 700

We can now write the system of equations in a simplified form:

3. 107x + 70y = 259
4. 70x + 70y = 700

To eliminate y, we will subtract equation 4 from equation 3:

(107x + 70y) - (70x + 70y) = 259 - 700 37x = -441

Dividing both sides by 37:

x = -441/37 x = -12

Now, substitute the value of x back into equation 1 to solve for y:

-12 + y = 10 y = 10 + 12 y = 22

Therefore, the solution to the system of equations is x = -12 and y = 22.