Question

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

Answer 1

Answer: x=2 and y=4/3

Step-by-step 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]

$y=\frac{8-2x}{3}$

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

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

$9x-3(\frac{8-2x}{3} )=14$                 [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]

$y=\frac{4}{3}$

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