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

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