Question

X-y=-5/7 4x+3y=-4 целых 6/7

Answer 1

Ответ:(-1; -2/7)

Пошаговое объяснение:

x-y=-5/7(*4)

4x+3y=-4 целых 6/7

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4x-4y=-20/7(1)

4x+3y=-34/7(2)

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вычитаем из 1 уравнения 2 уравнение

-7у=14/7

у=14/7:(-7)

у=14/7*(-1/7)

у=-2/7

подставим значение у в 1 уравнение

4x-4*(-2/7)=-20/7

4х-(-8/7)=-20/7

4х+8/7=-20/7

4х=-20/7-8/7

4х=-28/7

х=-28/7×1/4

х=-7/7=-1

проверим подставим значения х и у

-1-(-2/7)=-7/7+2/7=-5/7

4*(-1)+3*(-2/7)=-4-6/7=-4 целых 6/7

Answer 2

To solve the system of equations:

1. X - y = -5/7 .......(Equation 1)
2. 4x + 3y = -4 целых 6/7 .......(Equation 2)

Let's start by eliminating one variable from these equations. We can do this by multiplying both sides of Equation 1 by 3 and both sides of Equation 2 by 1 to make the coefficients of y the same in both equations:

1. 3(X - y) = 3(-5/7) Simplify: 3X - 3y = -15/7 .......(Equation 3)

2. 1(4x + 3y) = 1(-4 целых 6/7) Simplify: 4x + 3y = -4 целых 6/7 .......(Equation 4)

Now, we can add Equation 3 and Equation 4 to eliminate y:

(3X - 3y) + (4x + 3y) = -15/7 - 4 целых 6/7

Simplify: 3X + 4x = -15/7 - 4 целых 6/7

Combine the whole number and fractional parts: 3X + 4x = -4 целых (15/7 + 6/7)

Now, add the fractions together: 3X + 4x = -4 целых (21/7)

Simplify the whole number part: 3X + 4x = -4 целых 3/7 .......(Equation 5)

Now, let's find the common multiple of 3 and 4, which is 12. Multiply both sides of Equation 5 by 12 to eliminate the fractions:

12(3X + 4x) = 12(-4 целых 3/7)

Simplify: 36X + 48x = -48 целых 3/7

Combine the whole number and fractional parts: 36X + 48x = -48 целых (7*6/7)

Now, we can cancel out the fractional part in the parentheses: 36X + 48x = -48 целых 6

Next, combine the X terms on the left side: 36X + 48X = -48 целых 6

Simplify further: 84X = -48 целых 6

Finally, solve for X: X = (-48 целых 6) / 84

To simplify the fraction, divide the numerator and denominator by their greatest common divisor, which is 6:

X = (-8 целых 1) / 14

Now, we can simplify further by dividing both the numerator and the denominator by their greatest common divisor, which is 1:

X = -8 / 14

And the simplified fraction is:

X = -4 / 7

Now that we have the value of X, we can substitute it back into Equation 1 to find the value of y:

X - y = -5/7

-4/7 - y = -5/7

To isolate y, add 4/7 to both sides:

y = -5/7 + 4/7

y = -1/7

So, the solution to the system of equations is:

X = -4/7 y = -1/7