Question

solve for a and b: 47a+31b=63
31a+47b=15​

Answer 1

Step-by-step explanation:

45a+31b=63 ........ (1)

31a+47b=15 ......... (2)

By multiplying (1) by 47 and (2) by 31

Then, subtracting i from ii

And solve it

Answer 2

Answer:

(2, - 1)

Step-by-step explanation:

47a + 31b = 63

31a + 47b = 15

Cramer's rule:

Δ = $\left[\begin{array}{cc}47&31\\31&47\end{array}\right]$ = 47² - 31²  = (47 - 31)(47 + 31) = 16 × 78 = 1248

Δa = $\left[\begin{array}{cc}63&31\\15&47\end{array}\right]$ = 63×47 - 31×15 = 2496

Δb = $\left[\begin{array}{cc}47&63\\31&15\end{array}\right]$ = 47×15 - 63×31 = - 1248

a = Δa / Δ = 2496 ÷ 1248 = 2

b = Δb / Δ = - 1248 ÷ 1248 = - 1

(2 , - 1)