Question 1205723
.
Solve the system using the substitution method. If there is exactly one 
solution, write as an ordered pair. If not, choose one of the other options.
6x + 2y = 34
x = -4y + 24
A. One solution:
B. No solution
C. Infinite number of solutions
~~~~~~~~~~~~~~~~~~~~~~~


<pre>
You are lucky: you are given the system of equations, which is just ready for using the substitution method.


Indeed, the second equation expresses x implicitly via y.
So, substitute this expression of second equation into first equation.


You will get then

    6*(-4y+24) + 2y = 34.


Thus, you have now one equation with only one unknown y.

Simplify it and solve for y

    -24y + 144 + 2y = 34

    -24y + 2y = 34 - 144

        -22y  =    -110

           y  =    {{{(-110)/(-22)}}} = 5.


Thus you just found out one unknown y:  y = 5.


To find x, use the second given equation

    x = -4y + 24 = -4*5 + 24 = -20 + 24 = 4.


<U>ANSWER</U>.  The problem has one and only one solution  x= 4,  y= 5.


To check your solution, substitute these found values into equations
and make sure that in each equation the number in the left side is the same as in the right side.
</pre>

Solved, with all necessary explanations.



/////////////////////



From my post, learn how to write your problem, when you post it to this forum.


Do not use so many commas: they are unnecessary, so take them out.


Simply write each equation in separate line and do not use commas.
Also, do not use curved brackets: they also are unnecessary.



Happy learning (!)


Come again to this forum soon to learn something new.