2x - 6y = 6 6x - 4y = 2
2 answers:
9514 1404 393
Answer:
(x, y) = (-3/7, -1 1/7)
Step-by-step 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)
_____
<em>Additional comment</em>
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.
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