Question

Solve the system of equations by substitution. x + y = A system of equations. StartFraction 3 over 8 EndFraction x plus StartFraction one-third EndFraction y equals StartFractions 17 over 24 EndFraction. x + 7y = 8 ( , )

Answer 1

Answer:

(1,1)

Step-by-step explanation:

juss took it

Answer 2

Answer:

$x=1$ and $y=1$

Step-by-step explanation:

We have to solve by substitution the given system of equations:

$\left \{ {{\frac{3}{8}x+\frac{1}{3}y=\frac{17}{24} }\atop {x+7y=8}} \right.$

First, we have to choose an equation, no matter which one, and isolate a certain variable, no matter which one either. So, by our own criteria, we choose the second equation, and we'll isolate x:

$x+7y=8\\x=8-7y$

Now, this equivalence for x, we will replace it in the other equation, instead of x, we will put the result:

$\frac{3}{8}(8-7y)+\frac{1}{3}y=\frac{17}{24}$

Then, we solve for y:

$\frac{3}{8}(8-7y)+\frac{1}{3}y=\frac{17}{24}\\\frac{3}{8}8-\frac{3}{8}7y+\frac{1}{3}y=\frac{17}{24}\\-\frac{21}{8}y+\frac{1}{3}y=\frac{17}{24}-3\\\frac{-63y+8y}{24}=\frac{17-72}{24}\\ \frac{-55y}{24}=\frac{-55}{24}\\y=\frac{-55(24)}{24(-55)}=1$

Now, the final process will be to replace this y-value in one equation, no matter which one, and find x-value:

$x+7y=8\\\\x+7(1)=8\\x=8-7\\x=1$

Therefore, the solution of the system is $x=1$ and $y=1$