13×+22y = 1610

Question

32/× +12y = 22/10

Answer 1

To solve this system of equations, we can use the method of substitution.

From the second equation, we can rewrite it as:

32/x + 12y = 2.2

Next, we can multiply both sides of this equation by x to get rid of the fraction:

32 + 12xy = 2.2x

Now, we can rearrange this equation to solve for x:

2.2x - 12xy = 32

Factor out x:

x(2.2 - 12y) = 32

Divide both sides by (2.2 - 12y) to solve for x:

x = 32 / (2.2 - 12y)

Now, we can substitute this expression for x in the first equation:

13(32 / (2.2 - 12y)) + 22y = 1610

Multiply both sides of this equation by (2.2 - 12y) to eliminate the denominator:

13(32) + 22y(2.2 - 12y) = 1610(2.2 - 12y)

Simplify:

416 + 22y(2.2 - 12y) = 3542 - 19320y

Expand:

416 + 48.4y - 264y^2 = 3542 - 19320y

Rearrange this equation to form a quadratic equation:

264y^2 - 48.4y - 19320y + 3542 - 416 = 0

Combine like terms:

264y^2 - 19632y + 3126 = 0

Divide through the equation by 6 to simplify:

44y^2 - 3272y + 521 = 0

This is a quadratic equation that we can solve for y using factoring, completing the square, or the quadratic formula.