Question 196627


Start with the given system of equations:

{{{system(3x+2y=7,2x-y=4)}}}



{{{2(2x-y)=2(4)}}} Multiply the both sides of the second equation by 2.



{{{4x-2y=8}}} Distribute and multiply.



So we have the new system of equations:

{{{system(3x+2y=7,4x-2y=8)}}}



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(3x+2y)+(4x-2y)=(7)+(8)}}}



{{{(3x+4x)+(2y+-2y)=7+8}}} Group like terms.



{{{7x+0y=15}}} Combine like terms.



{{{7x=15}}} Simplify.



{{{x=15/7}}} Divide both sides by {{{7}}} to isolate {{{x}}}.



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{{{3x+2y=7}}} Now go back to the first equation.



{{{3(15/7)+2y=7}}} Plug in {{{x=15/7}}}.



{{{45/7+2y=7}}} Multiply.



{{{cross(7)(45/cross(7))+7(2y)=7(7)}}} Multiply EVERY term by the LCD {{{7}}} to clear any fractions.



{{{45+14y=49}}} Multiply.



{{{14y=49-45}}} Subtract {{{45}}} from both sides.



{{{14y=4}}} Combine like terms on the right side.



{{{y=(4)/(14)}}} Divide both sides by {{{14}}} to isolate {{{y}}}.



{{{y=2/7}}} Reduce.



So the solutions are {{{x=15/7}}} and {{{y=2/7}}} which form the ordered pair *[Tex \LARGE \left(\frac{15}{7},\frac{2}{7}\right)]