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28 votes
28 votes
2x - 6y = 6
6x - 4y = 2

User Hammad Akhwand
by
2.3k points

2 Answers

18 votes
18 votes

Answer:

x = - 3/7

y = - 8/7

Explanation:

(2x - 6y = 6)/2 =

x - 3y = 3

x = 3y + 3

Substitution:

6 (3y +3) - 4y = 2

18y + 18 - 4y = 2

14y = -18+2

y = -16/14

y = - 8/7

Substitution:

x = 3(-8/7)+3

x = -24/7 + 3

x = -3/7

User Giankotarola
by
2.6k points
11 votes
11 votes

9514 1404 393

Answer:

(x, y) = (-3/7, -1 1/7)

Explanation:

We can divide each equation by 2 and subtract the constant to put them in general form.

x -3y -3 = 0

3x -2y -1 = 0

This form facilitates use of the "cross multiplication method" of solution. That method tells us ...

1/d1 = x/d2 = y/d3

where the differences d1, d2, d3 are the differences of cross-products:

d1 = 1(-2) -(3(-3)) = 7

d2 = -3(-1) -(-2(-3)) = -3

d3 = -3(3) -(-1(1)) = -8

Then the solutions are ...

x = d2/d1 = -3/7

y = d3/d1 = -8/7

(x, y) = (-3/7, -8/7)

_____

Additional comment

When the general form equations ax+by+c=0 and dx+ey+g=0 have their coefficients written in two rows: (note the repeated first coefficient)

  • a, b, c, a
  • d, e, g, d

The pattern in the cross-differences is relatively easy to see:

  • d1 = ae -db
  • d2 = bg -ec
  • d3 = cd -ga

The expressions for the solution values, (x, y) = (d2/d1, d3/d1), are substantially identical to those of Cramer's method.

2x - 6y = 6 6x - 4y = 2-example-1
User Ambili B Menon
by
2.7k points