Question 229941
{{{x-2y=3}}}  Equation A
{{{5x+4y=8}}}  Equation B


Step 1.  Multiply Equation A by 2 to both sides of the equation 


{{{2x-4y=6}}} Equation A1
{{{5x+4y=8}}}  Equation B


Step 2.  Add Equations A1 and B to get rid of the y-terms


{{{2x+5x-cross(4y)+cross(4y)=6+8}}}


{{{7x=14}}}


Step 3.  Divide by seven to both sides of the equation


{{{cross(7)x/cross(7)=14/7}}}


{{{x=2}}}


Step 4.  Substitute {{{x=2}}} into Equation A {{{x-2y=3}}} to get y


{{{2-2y=3}}}


Add 2y-3 to both sides of the equation


{{{2-cross(2y)+cross(2y)-3=cross(3)+2y-cross(3)}}}


{{{-1=2y}}}


Divide by 2 to both sides of the equation


{{{-1/2=cross(2)y/cross(2)}}}


{{{y=-1}}}


Check solution {{{x=2}}} and {{{y=-1/2}}} into Equation B {{{5x+4y=8}}} 


{{{5*2+4*(-1/2)=8}}}


{{{10-2=8}}}


{{{8=8}}} which is a true statement.


Step 5.  ANSWER:  The solution is {{{x=2}}} and {{{y=-1/2}}} or (2, -1/2) our intersection point.


I hope the above steps were helpful.


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Respectfully,
Dr J

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