Question 173903
Your system:

{{{2x+5y=19}}}
{{{x=32-7y}}}


Your solution:

{{{2(32-7y)+5y=19}}}  Ok, spot on.
{{{64-14y+5y=19}}}  Still going well.
{{{20y=83}}}  Oops!  How did you manage to add {{{-14y}}} to {{{5y}}} and come up with {{{20y}}}? {{{-14y+5y=-9y}}}.  Also, you subtracted 64 from the left side, but added it to the right side.  You need to subtract 64 from both sides.


{{{64-14y+5y=19}}}


{{{-9y=19-64}}}


{{{-9y=-45}}}


{{{y=5}}}


Half done.  Now you need to go back and use this value for {{{y}}} to calculate the value for {{{x}}} that satisfies both equations.


So take {{{x=32-7y}}} and substitute {{{5}}} for {{{y}}}.


{{{x=32-7(5)=32-35=-3}}}


Now you can write your ordered pair because you have an {{{x}}} value and a corresponding {{{y}}} value.


The solution set for your system is ({{{-3}}},{{{5}}}).


Ah, ah, ah...not so fast.  We still need to check the answers.  Substituting the values of x and y into both equations must result in two true statements.  Let's see:


{{{2(-3)+5(5)=-6+25=19}}}  True


{{{-3=32-7(5)=-3}}} True


Answer checks.