Question

1) 2x+y=7 x(2)-xy=6 2) x(2)-y(2)=16 x+y=2

Answer 1

Если это система то × получается 14/4

Answer 2

Let's solve each system of equations step by step:

Equation 1: 2x + y = 7 Equation 2: x(2) - xy = 6

To eliminate the variable 'y', we can multiply Equation 1 by 2 and subtract it from Equation 2:

2 * (2x + y) = 2 * 7 4x + 2y = 14

(4x + 2y) - (x(2) - xy) = 14 - 6 4x + 2y - 2x + xy = 8

Combining like terms: 2x + 2y + xy = 8

Now, let's rearrange the equation: xy + 2x + 2y = 8

We can factor out 'x' and 'y' terms: x(y + 2) + 2(y + 2) = 8 (x + 2)(y + 2) = 8

Divide both sides by (y + 2): (x + 2)(y + 2) / (y + 2) = 8 / (y + 2) x + 2 = 8 / (y + 2)

Subtract 2 from both sides: x = 8 / (y + 2) - 2

Now we can substitute this value of 'x' into Equation 1:

2x + y = 7 2(8 / (y + 2) - 2) + y = 7 16 / (y + 2) - 4 + y = 7

Multiply both sides by (y + 2): 16 - 4(y + 2) + y(y + 2) = 7(y + 2)

Expand and simplify: 16 - 4y - 8 + y^2 + 2y = 7y + 14

Rearrange to form a quadratic equation: y^2 - 11y + 22 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula.

Equation 1: x(2) - y(2) = 16 Equation 2: x + y = 2

To eliminate the variable 'x', we can square Equation 2:

(x + y)^2 = 2^2 x^2 + 2xy + y^2 = 4

Now we can substitute this value into Equation 1:

x^2 + 2xy + y^2 - y^2 = 16 x^2 + 2xy = 16

Subtract 2xy from both sides: x^2 = 16 - 2xy

Substitute the value of x from Equation 2 into the above equation:

(2 - y)^2 = 16 - 2(2 - y)y 4 - 4y + y^2 = 16 - 4y + 2y^2

Simplify and rearrange: 2y^2 - y^2 - 4y + 4y + 16 - 4 = 0 y^2 - 4 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula.