document.write( "Question 253710: Solve each system by substitution
\n" ); document.write( "3x+y=-8
\n" ); document.write( "-2x-y=6 \n" ); document.write( "

Algebra.Com's Answer #186043 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( "Start with the given system of equations:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"system%283x%2By=-8%2C-2x-y=6%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So let's isolate y in the first equation\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3x%2By=-8\"$ Start with the first equation\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-8-3x\"$ Subtract $\"3x\"$ from both sides\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-3x-8\"$ Rearrange the equation\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since $\"y=-3x-8\"$ , we can now replace each $\"y\"$ in the second equation with $\"-3x-8\"$ to solve for $\"x\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"-2x-highlight%28%28-3x-8%29%29=6\"$ Plug in $\"y=-3x-8\"$ into the second equation. In other words, replace each $\"y\"$ with $\"-3x-8\"$ . Notice we've eliminated the $\"y\"$ variables. So we now have a simple equation with one unknown.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"-2x%2B3x%2B8=6\"$ Distribute the negative\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%2B8=6\"$ Combine like terms on the left side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=6-8\"$ Subtract 8 from both sides\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=-2\"$ Combine like terms on the right side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------First Answer------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the first part of our answer is: $\"x=-2\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since we know that $\"x=-2\"$ we can plug it into the equation $\"y=-3x-8\"$ (remember we previously solved for $\"y\"$ in the first equation).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-3x-8\"$ Start with the equation where $\"y\"$ was previously isolated.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-3%28-2%29-8\"$ Plug in $\"x=-2\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=6-8\"$ Multiply\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-2\"$ Combine like terms \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------Second Answer------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the second part of our answer is: $\"y=-2\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------Summary------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our answers are:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=-2\"$ and $\"y=-2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "which form the point

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's graph the two equations (if you need help with graphing, check out this solver)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From the graph, we can see that the two equations intersect at

. This visually verifies our answer.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

graph of $\"3x%2By=-8\"$ (red) and $\"-2x-y=6\"$ (green) and the intersection of the lines (blue circle).
\n" ); document.write( " \n" ); document.write( "

\n" );