Question 117668
Steps to solve a system of equations by the substitution method:
In general, if you solve a system of equations and the result is a true statement, such as {{{- 8 = -8}}}, the system has{{{ infinitely}}} many {{{solutions}}}; if the result is a false statement, such as {{{- 5 = 7}}}, the system has {{{no}}}{{{ solution}}}.
We will start with an example to show the steps in solving a system of equations by the substitution method:

Use substitution to solve the system of equations #{{{1}}}-> {{{ x + y = 1}}} and #{{{2}}}-> {{{2x + y = - 1}}}. 
Step 1: 
Solve one of the equations for {{{ x}}} or {{{y}}}. Let it be: solve for {{{x}}} from equation #{{{1.}}} since the coefficient of {{{x}}} is {{{1}}}.
{{{x + y = 1}}} 
{{{x = 1- y }}}
Step 2:
 Substitute this value into the other equation. Use the #{{{2.}}}equation.
{{{2x + y = - 1}}}……………………. use the #{{{2.}}} equation.
{{{2(1 - y) + y = -1}}}……………..substitute {{{1 – y}}} for {{{x}}}

{{{2 - 2y + y = -1}}}…………………….. distribute

Step 3:
 Solve this equation. 
{{{2 - 2y + y = -1}}}………………………….. solve for {{{y}}} 
{{{-y = -3}}} ……………………..divide both sides by {{{-1}}}
{{{y = 3}}}
Step 4: 
Find the value of the other variable using substitution into either equation. 
{{{x + y = 1}}}	………. use the #{{{1.}}} equation
{{{x + 3 = 1}}}………………substitute {{{3}}} for {{{y}}}

{{{x = -2}}}…………………….solution for {{{x}}}

The solution to the {{{system}}} is:
 ({{{x}}},{{{y}}}) = ({{{-2}}},{{{3}}}) 
Check: Substitute {{{-2}}} for {{{x}}} and {{{3}}} for {{{y}}} in each of the original equations and check for true statements.