Solve these simultaneous linear equation
3x - 4y = 1
6x + 7y = 13​

9514 1404 393

  (x, y) = (59/45, 11/15) ≈ (1.311, 0.733)

Step-by-step explanation:

A graphing calculator shows us the solution is not integer values, so we may find it easiest to solve these equations using the "cross-multiplication method."

Writing the equations in general form, we have ...

  3x -4y -1 = 0

  6x +7y -13 = 0

Then we can form an array of the coefficients, repeating the first column:

Forming differences of cross products involving adjacent pairs of columns gives ...

  d1 = (3)(7) -(6)(-4) = 45

  d2 = (-4)(-13) -(7)(-1) = 59

  d3 = (-1)(6) -(-13)(3) = 33

Then the solutions are found from ...

  1/d1 = x/d2 = y/d3

or

  x = d2/d1 = 59/45

  y = d3/d1 = 33/45 = 11/15

The solution is (x, y) = (59/45, 11/15) ≈ (1.311, 0.733).

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Additional comment

This takes longer to explain than to do. One reason we like it is that the number of math operations is slightly smaller than the number of math operations required for substitution or elimination. It is especially nice when the solution is not a pair of integers.

no solution exists the way you wrote the equation.