9514 1404 393
Answer:
(x, y) = (3, 2)
Step-by-step explanation:
These look like solution using elimination or substitution could be tedious, so we'll use the "cross multiplication" technique for solution. This requires each equation be in general form: ax+by+c = 0.
The first equation can be multiplied by 6 and 13 subtracted.
x/2 +y/3 = 13/6
3x +2y = 13
3x +2y -13 = 0
The second equation can be multiplied by 28 and 10 subtracted.
2x/7 -y/4 = 5/14
8x -7y = 10
8x -7y -10 = 0
Now, an array of coefficients can be constructed. The last column is the same as the first.
[tex]\begin{array}{cccc}3&2&-13&3\\8&-7&-10&8\end{array}[/tex]
Cross-multiplying adjacent columns, we can write the equation ...
1/(3(-7)-8(2)) = x/(2(-10)-(-7)(-13)) = y/(-13(8)-(-10)(3))
1/-37 = x/-111 = y/-74
Solving for x and y, we have ...
x = -111/-37 = 3
y = -74/-37 = 2
The solution is (x, y) = (3, 2).
