Question

Solve this simultaneous equation x/2+ y/3=13/6 2x/7-y/4=5/14

Answer 1

9514 1404 393

Answer:

(x, y) = (3, 2)

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.

`\begin{array}{cccc}3&2&-13&3\\8&-7&-10&8\end{array}`

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).