[tex]x+y=1\\x-2y=4[/tex]
Solve the equation for [tex]x[/tex]
[tex]x=1 -y\\\\x-2y=4[/tex]
Substitute the given value of x into the equation [tex]x-2y=4[/tex]
[tex]1-y-2y=4[/tex]
Collect like terms
[tex]1-3y=4[/tex]
Move constant to the right hand side and change its sign
[tex]-3y=4-1[/tex]
Subtract the numbers
[tex]-3y=3[/tex]
Divide both sides of the equation by [tex]-3[/tex]
[tex]y=-1[/tex]
Substitute the given value of [tex]y[/tex] into the equation [tex]x=1-y[/tex]
[tex]x=1-(-1)[/tex]
When there is a _ in front of an expression in parentheses , change the sign of each term of the expression
[tex]x=1+1[/tex]
Add the numbers
[tex]x=2[/tex]
The possible solution of the system is the ordered pair [tex](x,y)[/tex]
[tex](x,y)= (2,-1)[/tex]
Check if the given ordered pair is the solution of the system of equations
[tex]2-1=1\\2-2x(-1)=4[/tex]
Simplify the equalities
[tex]1=1\\4=4[/tex]
Since all of the equalities are true, the ordered pair is the solution of the system
[tex](x,y)=(2,-1)[/tex]
Answer: [tex](x,y) = (2,-1)[/tex]
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