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.
[tex]2x+3y=8[/tex] [subtract both sides by 2x]
[tex]3y=8-2x[/tex] [divide both sides by 3]
[tex]y=\frac{8-2x}{3}[/tex]
Now that we have y, we can plug it into the second equation.
[tex]9x-3y=14[/tex] [plug in y]
[tex]9x-3(\frac{8-2x}{3} )=14[/tex] [multiply 3 and y to cancel out the 3]
[tex]9x-(8-2x)=14[/tex] [distribute -1 to 8-2x]
[tex]9x-8+2x=14[/tex] [combine like terms]
[tex]11x-8=14[/tex] [add both sides by 8]
[tex]11x=22[/tex] [divide both sides by 11]
[tex]x=2[/tex]
Since we know the value of x, we can substitute it back into any of the 2 equations to find y.
[tex]2x+3y=8[/tex] [plug in x=2]
[tex]2(2)+3y=8[/tex] [multiply 2 and 2]
[tex]4+3y=8[/tex] [subtract both sides by 4]
[tex]3y=4[/tex] [divide both sides by 3]
[tex]y=\frac{4}{3}[/tex]
Our final answer is x=2 and y=4/3.
