Question

solve using cramer's rule: 5x+3y=9, 4y+7x=13

Answer 1

Step-by-step explanation:

The system of equation can be written in matrix form (i.e., AX = B) as shown below.

[354−3][xy]=[213]

Here, A =[354−3] and B=[213]

To find the solution by Cramer's method we define two matrices B1 and B2. The matrix B1 is obtained by replacing first column of matrix A by the column in B. similarly B2 is obtained by replacing column 2 of matrix A by the column in B.

That is, B1=[2134−3],B2=[35213]

Now, x =|B1||A|

=∣∣∣2134−3∣∣∣∣∣∣354−3∣∣∣=2−(3)−4(13)3(−3)−4(5)

=−6−52−9−20=5829=2

and,

y=|B2||A|=∣∣∣35213∣∣∣∣∣∣354−3∣∣∣

=3×13−2×53(−3)−4×5=29−29=−1

Thus, in general for a system of linear equations px + qy =a, rx + sy = b, solution by Cramer's method is

x=∣∣∣abqs∣∣∣∣∣∣prqs∣∣∣,y=∣∣∣prab∣∣∣∣∣∣prqs∣∣∣

Answer 2

Answer:

Reffer above the attachment