maths

posted by .

The variables x and y satisfy the equations
2/x−24/y=−1
and
6/x+33/y=2.
Find the product xy.

  • maths -

    2 / x − 24 / y = − 1 Divide both sides by 2

    1 / x - 12 / y = - 1 / 2 Add 12 / y to both sides

    1 / x - 12 / y + 12 / y = - 1 / 2 + 12 / y

    1 / x = 12 / y - 1 / 2


    6 / x + 33 / y = 2

    6 * ( 12 / y - 1 / 2 ) + 33 / y = 2

    72 / y - 6 * 1 / 2 + 33 / y = 2

    72 / y - 3 + 33 / y = 2

    105 / y - 3 = 2 Add 3 to both sides

    105 / y - 3 + 3 = 2 + 3

    105 / y = 5 Divide both sides by 5

    21 / y = 1 Multipy both sides by y

    y * 21 / y = 1 * y

    21 = y

    y = 21


    1 / x = 12 / y - 1 / 2

    1 / x = 12 / 21 - 1 / 2

    1 / x = 3 * 4 / ( 3 * 7 ) - 1 / 2

    1 / x = 4 / 7 - 1 / 2

    1 / x = 8 / 14 - 7 / 14

    1 / x = 1 / 14

    Reciprocal:

    x = 14



    x * y = 14 * 21 = 294

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Find an equation for the surface consisting of all points P(x, y, z) equidistant from the point P(0, 1, 0) and the plane x = 3. Answer Choices: 1. y2 + z2 − 6x + 2y − 8 = 0 2. x2 + z2 + 6y − 2z − 8 = 0 3. y2 …
  2. Math

    Find a system of linear equations corresponding to the following augmented matrices: (a) 2 0 |0 3 −4 |0 0 1 |1 (b) 3 0 −2 |5 7 1 4 |−3 0 −2 1 |7 (c) 7 2 1 −3 |5 1 2 4 0 |1 (d) 1 0 0 0 |7 0 1 0 0 |−2 …
  3. algebra

    The variables x and y satisfy the equations 2/x−24/y=−1 and 6/x+33/y=2. Find the product xy.
  4. biology

    Given the part of the molecule shown below, can the underlined atom participate in a hydrogen bond with an approriate bonding partner?
  5. Product of Roots of Sums of Products of Difference

    What is the product of all roots to the equation ++(x−1)(x−2)(x−3)+(x−2)(x−3)(x−4)(x−3)(x−4)(x−5)+(x−4)(x−5)(x−6)(x−5)(x−6)(x−7)+(x−6)(x−7)(x−8)=0?
  6. Product of Roots of Sums of Products of Difference

    What is the product of all roots to the equation ++(x−1)(x−2)(x−3)+(x−2)(x−3)(x−4)(x−3)(x−4)(x−5)+(x−4)(x−5)(x−6)(x−5)(x−6)(x−7)+(x−6)(x−7)(x−8)=0?
  7. mathematics

    x,y and z are complex numbers that satisfy the equations x+y+z=2, xy+yz+zx=3 and xyz=4. Given that 1/(1−x−yz)+1(1−y−zx)+1(1−z−xy)=ab, where a and b are coprime positive integers, what is the value …
  8. MATHS

    The number 2+3√+5√−−−−−−−−−−√ is algebraic because it is a root of a monic polynomial of degree 8, namely x^8+ax^7+bx^6+cx^5+dx^4+ex^3+fx^2+g^x+h. Find |a|+|b|+|c|+|d|+|e|+|f|+|g|+|h|.
  9. math

    The number 27+200−−−√−−−−−−−−−√ can be simplified to the form a+b√, where a and b are positive integers. Find the product ab.
  10. math

    Completely factor the expression 2a3 − 128. A. 2(a − 4)3 B. 2(a − 4)(a2 + 4a + 16) C. 2(a3 − 64) D. Prime Completely factor the expression 7(x − y) − z(x − y). A. Prime B. (x − y)(7 − …

More Similar Questions