Question 151611
In order to find the answer, let's check all of the possible answers (note: an alternative is to solve the system)


A)



Let's see if (2,3) is a solution.



{{{y=3x+1}}} Start with the first equation.



{{{(3)=3*(2)+1}}} Plug in {{{x=2}}} and {{{y=3}}}.



{{{3=3*(2)+1}}} Evaluate and simplify the left side.



{{{3=7}}} Evaluate and simplify the right side.



Since the equation is <font size="4"><b>not</b></font> true, this means that (2,3) is <font size="4"><b>not</b></font> a solution.



Let's see if (2,3) is a solution.



{{{y=5x-3}}} Start with the second equation.



{{{(3)=5*(2)-3}}} Plug in {{{x=2}}} and {{{y=3}}}.



{{{3=5*(2)-3}}} Evaluate and simplify the left side.



{{{3=7}}} Evaluate and simplify the right side.



Since the equation is <font size="4"><b>not</b></font> true, this means that (2,3) is <font size="4"><b>not</b></font> a solution.



Since at least one of the equations of the system is false, this means that (2,3) is <font size="4"><b>not</b></font> a solution. Remember, a solution must satisfy  <font size="4"><b>all</b></font> of the equations in the system.



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B)




Let's see if (0,1) is a solution.



{{{y=3x+1}}} Start with the first equation.



{{{(1)=3*(0)+1}}} Plug in {{{x=0}}} and {{{y=1}}}.



{{{1=3*(0)+1}}} Evaluate and simplify the left side.



{{{1=1}}} Evaluate and simplify the right side.



Since the equation is <font size="4"><b>true</b></font>, this means that (0,1) is a solution.



Let's see if (0,1) is are a solution.



{{{y=5x-3}}} Start with the second equation.



{{{(1)=5*(0)-3}}} Plug in {{{x=0}}} and {{{y=1}}}.



{{{1=5*(0)-3}}} Evaluate and simplify the left side.



{{{1=-3}}} Evaluate and simplify the right side.



Since the equation is <font size="4"><b>not</b></font> true, this means that (0,1) is <font size="4"><b>not</b></font> a solution.



Since at least one of the equations of the system is false, this means that (0,1) is <font size="4"><b>not</b></font> a solution. Remember, a solution must satisfy  <font size="4"><b>all</b></font> of the equations in the system.



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C)



Let's see if (1,2) is a solution.



{{{y=3x+1}}} Start with the first equation.



{{{(2)=3*(1)+1}}} Plug in {{{x=1}}} and {{{y=2}}}.



{{{2=3*(1)+1}}} Evaluate and simplify the left side.



{{{2=4}}} Evaluate and simplify the right side.



Since the equation is <font size="4"><b>not</b></font> true, this means that (1,2) is <font size="4"><b>not</b></font> a solution.



Let's see if (1,2) is a solution.



{{{y=5x-3}}} Start with the second equation.



{{{(2)=5*(1)-3}}} Plug in {{{x=1}}} and {{{y=2}}}.



{{{2=5*(1)-3}}} Evaluate and simplify the left side.



{{{2=2}}} Evaluate and simplify the right side.



Since the equation is <font size="4"><b>true</b></font>, this means that (1,2) is a solution.



Since at least one of the equations of the system is false, this means that (1,2) is <font size="4"><b>not</b></font> a solution. Remember, a solution must satisfy  <font size="4"><b>all</b></font> of the equations in the system.



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D)





Let's see if (2,7) is a solution.



{{{y=3x+1}}} Start with the first equation.



{{{(7)=3*(2)+1}}} Plug in {{{x=2}}} and {{{y=7}}}.



{{{7=3*(2)+1}}} Evaluate and simplify the left side.



{{{7=7}}} Evaluate and simplify the right side.



Since the equation is <font size="4"><b>true</b></font>, this means that (2,7) is a solution.



Let's see if (2,7) is a solution.



{{{y=5x-3}}} Start with the second equation.



{{{(7)=5*(2)-3}}} Plug in {{{x=2}}} and {{{y=7}}}.



{{{7=5*(2)-3}}} Evaluate and simplify the left side.



{{{7=7}}} Evaluate and simplify the right side.



Since the equation is <font size="4"><b>true</b></font>, this means that (2,7) is a solution.



Since <font size="4"><b>all</b></font> of the equations of the system are true, this means that (2,7) is a solution




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Answer:


So the solution is D) (2,7)