Question

solve the following pair of linear equation 41x+53y=135 and 53x+41y=147​

Answer 1

ANSWER:

x = 2, y = 1

GIVEN:

41x + 53y = 135

53x + 41y= 147

TO FIND:

x and y

EXPLANATION:

ADD THE TWO EQUATIONS, WE WILL GET

94x + 94y = 282

DIVIDE BY 94 ON BOTH SIDES

x + y = 3

SUBTRACT THE EQUATIONS, WE WILL GET

-12x + 12y = -12

DIVIDE BY -12 ON BOTH SIDES, WE WILL GET

x - y = 1

NOW WE GOT NEW TWO EQUATIONS

x - y = 1 --------> 1

x + y = 3 -------->2

ADD THE TWO NEW EQUATIONS, WE WILL GET

2x = 4

x = 2

SUBSTITUTE x = 2 IN x - y = 1

2 - y = 1

y = 2 - 1

y = 1

VERIFICATION:

SUBSTITUTE x = 2 AND y = 1 IN 41x + 53y = 135

41(2) + 53(1) = 82 + 53 = 135

SUBSTITUTE x = 2 AND y = 1 IN 53x + 41y = 147

53(2) + 41(1) = 106 + 41 = 147

THESE RESULTS COINCIDE WITH THE GIVEN QUESTION. HENCE OUR RESULT IS VERIFIED.

Answer 2

Answer:

41x+53y=135

53x+41y=147

Make the x-terms equal

53(41x+53y)=135x53

41(53x+41y)=147x41

=2173x + 2809y =7155

- 2173x + 1681y = 6027

1128y= 1128

y=1

Substitute

41x + 53(1)=135

41x=135-53

x = 82/41

x=2