Question 325293


Start with the given system of equations:


{{{system(-3x+3y=4,-x+y=3)}}}




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.





So let's isolate y in the second equation


{{{-x+y=3}}} Start with the second equation



{{{y=3+x}}} Add {{{x}}} to both sides



{{{y=x+3}}} Rearrange the equation



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Since {{{y=x+3}}}, we can now replace each {{{y}}} in the second equation with {{{x+3}}} to solve for {{{x}}}




{{{-3x+3highlight((x+3))=4}}} Plug in {{{y=x+3}}} into the second equation. In other words, replace each {{{y}}} with {{{x+3}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{-3x+3x+(3)(3)=4}}} Distribute {{{3}}} to {{{x+3}}}



{{{-3x+3x+9=4}}} Multiply



{{{9=4}}} Combine like terms on the left side



{{{0=4-9}}}Subtract 9 from both sides



{{{0=-5}}} Combine like terms on the right side



Since this equation is <font size=4><b>NEVER</b></font> true for any x value, this means there are no solutions.



So the system is inconsistent.