document.write( "Question 220150: solve trhe following system of equations using substitution.\r
\n" ); document.write( "\n" ); document.write( "2x + 3y = -1
\n" ); document.write( "5x - 2y = -12\r
\n" ); document.write( "\n" ); document.write( "(__,__)
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #165349 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
(Note: The solution provided by someone else did not use the substitution method.)
\n" ); document.write( "The substitution method:

Solve one equation (either one) for one of the variables (either one). So choose that variable and the equation that makes this step easiest.
Substitute into the other equation for that variable. This changes the equation into a one-variable equation.
Solve the one-variable equation for that variable.
Take the value for this variable and substitute it back into one of the original equations (either one). Once again a one-variable equation results.
Solve this one variable equation for the second variable

\n" ); document.write( "1. Solve an equation for one of the variables. The \"easy\" systems for the substitution method are the ones where a variable has a coefficient of 1 (or -1). Unfortunately this system is not an \"easy\" one. Since I prefer positives I'll solve the second equation for y:
\n" ); document.write( "5x - 2y = -12
\n" ); document.write( "Add 2y to both sides:
\n" ); document.write( "5x = 2y - 12
\n" ); document.write( "Add 12 to both side:
\n" ); document.write( "5x + 12 = 2y
\n" ); document.write( "Multiply both sides by 1/2 (or divide by two):
\n" ); document.write( " $\"%285%2F2%29x+%2B+6+=+y\"$

\n" ); document.write( "2. Substitute into the other equation:
\n" ); document.write( "2x + 3y = -1
\n" ); document.write( " $\"2x+%2B+3%28%285%2F2%29x+%2B+6%29+=+-1\"$
\n" ); document.write( "

\n" ); document.write( "3. Solve this equation.
\n" ); document.write( "Simplify.
\n" ); document.write( " $\"2x+%2B+%2815%2F2%29x+%2B+18+=+-1\"$
\n" ); document.write( " $\"%284%2F2%29x+%2B+%2815%2F2%29x+%2B+18+=+-1\"$
\n" ); document.write( " $\"%2819%2F2%29x+%2B+18+=+-1\"$
\n" ); document.write( "Subtract 18 from each side:
\n" ); document.write( " $\"%2819%2F2%29x+=+-19\"$
\n" ); document.write( "Multiply by 2/19 (or divide by 19/2):
\n" ); document.write( " $\"x+=+-2\"$

\n" ); document.write( "4. Substitute this solution back into one of the original equations:
\n" ); document.write( "2x + 3y = -1
\n" ); document.write( "2(-2) + 3y = -1

\n" ); document.write( "5. Solve this equation.
\n" ); document.write( "Simplify.
\n" ); document.write( "-4 + 3y = -1
\n" ); document.write( "Add 4 to both sides:
\n" ); document.write( "3y = 3
\n" ); document.write( "Multiply both sides by 1/3 (or divide by 3):
\n" ); document.write( "y = 1

\n" ); document.write( "So the solution is the point (-2, 1) \n" ); document.write( "

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