Question

2x+3y=8 9x-3y = 14
solve by substitution ​

Answer 1

Answer: x=2 and y=4/3

Explanation:

To solve by substitution method, you want to solve for one variable, and plug it into the other equation.

Let's solve for y in 2x+3y=8.

`2x+3y=8` [subtract both sides by 2x]

`3y=8-2x` [divide both sides by 3]

`y=(8-2x)/(3)`

Now that we have y, we can plug it into the second equation.

`9x-3y=14` [plug in y]

`9x-3((8-2x)/(3) )=14` [multiply 3 and y to cancel out the 3]

`9x-(8-2x)=14` [distribute -1 to 8-2x]

`9x-8+2x=14` [combine like terms]

`11x-8=14` [add both sides by 8]

`11x=22` [divide both sides by 11]

`x=2`

Since we know the value of x, we can substitute it back into any of the 2 equations to find y.

`2x+3y=8` [plug in x=2]

`2(2)+3y=8` [multiply 2 and 2]

`4+3y=8` [subtract both sides by 4]

`3y=4` [divide both sides by 3]

`y=(4)/(3)`

Our final answer is x=2 and y=4/3.