Question

Plz answer......


Find a and b
Form original simultaneous equations having this solution ​

Answer 1

Answer:

Step-by-step explanation:

If the system of simultaneous equations is

cx + dy = g

ex + fy = h

then the relevant determinants are

$D_x=\left|\begin{array}{cc}g&d\\h&f\end{array}\right|,\quad D_y=\left|\begin{array}{cc}c&g\\e&h\end{array}\right|,\quad D=\left|\begin{array}{cc}c&d\\e&f\end{array}\right|$

Notice that D is just the determinant made from the coefficients.  Then Dₓ is obtained by replacing the first column (the x coefficients) with the values at the right in the system of equations.  Similarly for the third determinant.

So the given determinants correspond to the system:

x + 2y = -1

2x - 3y = 12

Furthermore, a = 2 and b = 2.

Check

We didn't need the information about the solution to work out what a and b were.  But since we have them, let's check.

We should get x = Dₓ / D.

Dₓ = (-1)(-3) - 12a = 3 - 24 = -21

D = (1)(-3) - (2)(2) = -3 - 4 = -7

So x = Dₓ / D = (-21) / (-7) = 3.  Good... this matches the given information.

Similarly,

D_y = (1)(12) - (-1)b = 12 + 2 = 14

so y = 14 / (-7) = -2.  This also matches the given information.