Question

How would you substitute 2x+3y=12 and 4x=10+y

Answer 1

x = 3, y = 2

Explanation:

`\left\{\begin{array}{ccc}2x+3y=12\\4x=10+y&\text{subtract 10 from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}2x+3y=12&(1)\\4x-10=y&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\\\2x+3(4x-10)=12\qquad\text{use the distributive property}\\2x+(3)(4x)+(3)(-10)=12\\2x+12x-30=12\qquad\text{add 30 to both sides}\\14x-30+30=12+30\\14x=42\qquad\text{divide both sides by 14}\\\\(14x)/(14)=(42)/(14)\\\\x=3`

`\text{Put it ot (2):}\\\\y=4(3)-10\\y=12-10\\y=2`