Solve the following by substitution:

- \( x + y = 10 \)
- \( x - y = 5 \)

{ x + y = 10 x − y = 5 ​ { y = 10 − x x − y = 5 ​ { y = 10 − x x − ( 10 − x ) = 5 ​ { y = 10 − x x − 10 + x = 5 ​
{ y = 10 − x 2 x − 10 = 5 ​ { y = 10 − x 2 x = 5 + 10 ​ { y = 10 − x 2 x = 15 / : 2 ​ { y = 10 − x x = 2 15 ​ ​
{ y = 10 − 7 2 1 ​ x = 7 2 1 ​ ​ { y = 2 2 1 ​ x = 8 2 1 ​ ​

Answered by Lilith | 2024-06-10

Your question is -
x + y = 10 x - y = 5
Now, let us solve this system by the substitution method.
According to equation 2 ,
x - y = 5
thus, x = 5 + y
Substituting the value of x in equation 1,
(5 + y) + y = 10
5 + 2y = 10
2y = 10 - 5 = 5
thus, y = 5/2
Substituting the value of y in value of x,
x = 5 + y
= 5 + 5/2
= 15/2
Thus, x = 15/2 ( or 7.5) y = 5/2 ( or 2.5)

Answered by tadvisohil886 | 2024-06-10

By substituting y = 10 − x into the second equation x − y = 5 , we solve for x to find x = 7.5 and then substitute back to find y = 2.5 . Thus, the solution is x = 7.5 and y = 2.5 .
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Answered by Lilith | 2024-12-23