Question

2x+3y=5
- x+2y=8
subachtution
Method​

Answer 1

x = -2, y = 3 → (-2, 3)

Explanation:

`\left\{\begin{array}{ccc}2x+3y=5\\-x+2y=8&\text{subtract}\ 2y\ \text{from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}2x+3y=5\\-x=-2y+8&\text{change the signs}\end{array}\right\\\\\left\{\begin{array}{ccc}2x+3y=5&(1)\\x=2y-8&(2)\end{array}\right\\\\\text{Substitute (2) to (1)}:\\\\2(2y-8)+3y=5\qquad\text{use the distributive property}\\\\(2)(2y)+(2)(-8)+3y=5\\\\4y-16+3y=5\qquad\text{add 16 to both sides}\\\\4y+3y=5+16\\\\7y=21\qquad\text{divide both sides by 7}\\\\\boxed{y=3}`

`\text{Put it to (2)}\\\\x=2(3)-8\\\\x=6-8\\\\\boxed{x=-2}`