Question

Given the system of equations, what is the solution?5x - 4y = 7x = 5 - 3/2y

Answer 1

9514 1404 393

Answer:

  (x, y) = (61/23, 36/23)

Step-by-step explanation:

We assume you intend the equations to be ...

• 5x -4y = 7
• x = 5 -3/2y

Then in general form, they are ...

  5x -4y -7 = 0

  2x +3y -10 = 0

The solution using the "cross multiplication method" is ...

  1/(15 +8) = x/(40+21) = y/(-14 +50)

  (x, y) = (61/23, 36/23)

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Comment on "cross multiplication method"

When the coefficients from the general form equations are written as a 2×4 array with the first and last columns the same ...

  $\left\{\begin{array}{cccc}5&-4&-7&5\\2&3&-10&2\end{array}\right\}$

the solution is 1/d1 = x/d2 = y/d3, where d1, d2, d3 are the determinants of successive pairs of columns.

• d1 = (5)(3) -(2)(-4)
• d2 = (-4)(-10) -(3)(-7)
• d3 = (-7)(2) -(-10)(5)