use cramer's rule when solving each system?

Question

7x - 5y = 8
4x + 3y = 2

Answer 1

if you have two equations
ax+by=c
dx+ey=f
cramer's rule says the solution for x is

|c b|
|f e|
------
|a b|
|d e|

and y will be

|a c|
|d f |
------
|a b|
|d e|

where the the | indicate determinate

So, x will be

| 8 -5 |
| 2 3 |
-------
| 7 -5 |
| 4 3|

do the determinates

[(8*3)-(-5*2)]/[7*3-(-5*4)] = 34/41

y will be (note the denominator will be the same)
| 7 8 |
| 4 2 |
---------
| 7 -5 |
| 4 3 |

numerator is
(7*2)-(8*4) = -18
y=-18/41

x = 34/41
y = -9/41

Answer 2

First placed those right into a matrix: [a million -4 a million] [2 3 thirteen] Now i'm in simple terms going to place in writing it is Ax = b sort: [a million -4] [x] = [a million] [2 3] [y].....[thirteen] So Cramer's Rule says that: x = det(A?) / det(A) y = det(A?) / det(A) First locate the det(A): (a million)(3) - (-4)(2) = eleven Now locate det(A?). A? is in simple terms changing column a million with the b vector: A? = [a million -4] [thirteen 3] det(A?) = (a million)(3) - (-4)(thirteen) = fifty 5 Now locate det(A?): A?= [a million a million] [2 thirteen] det(A?) = eleven So we've each and every little thing we %: x = det(A?) / det(A) = fifty 5/eleven = 5 y = det(A?) / det(A) = eleven/eleven = a million The coordinate pair could be: (5, a million) <==answer

Answer 3

7x - 5y = 8
4x + 3y = 2

a b c d x y e f
[[7,-5][4,3]] [[x][y]] = [[8][2]]

A = [[7,-5][4,3]]
[[a,b][c,d]]

Aix = [[8,-5][2,3]]
[[e,b][f,d]]

Aiy = [[7,8][4,2]]
[[a,e][c,f]]

x = Det(Aix) / Det(A)
y = Det(Aiy) / Det(A)

x =Det( [[8,-5][2,3]]) / Det([[7,-5][4,3]] )take the determinate of both matrices
x = 8*3 - (-5)*2 / 7*3 - (-5)*4
x = 34/41


y = Det([[7,8][4,2]]) / Det([[7,-5][4,3]]) take the determinate of both matrices
y = 7*2 - 8*4 / 7*3 - (-5)*4
y = -18/41