Question 214867
Solve by the elimination method

0.3x-0.2y=4  Equation A
0.4x+0.5y=-29/19  Equation B


Step 1.  Let's get rid of the fraction in Equation A by multiplying by 10 to both sides of equation to get


{{{10*(0.3x-0.2y)=10*4}}}


{{{3x-2y=40}}}   Equation A-1


Step 2.  Let's get rid of the fraction in Equation B by multiplying by 190 to both sides of equation to get


{{{190(0.4x+0.5y)=-190*29/19}}}


{{{76x+95y=-290}}}  Equation B-1


Step 3.  Multiply Equation A-1 by -47.5


{{{47.5(3x-2y)=47.5*40}}} 


{{{142.5x-95y=1900}}}  Equation A-2


Step 4. Add Equation B-1 and Equation A-2 to eliminate y to get


{{{218.5x=1610}}}


{{{x=7.368421}}}


Substitute x into {{{3x-2y=40}}} will yield


{{{3*7.368421-2y=40}}}


{{{22.105263-2y=40}}}


{{{2y=-17.894737}}}


{{{y=-8.9473685}}}


Step 5.  ANSWER is {{{x=7.368421}}} and {{{y=-8.9473685}}}


As a check let's solve this using substituion.


*[invoke linear_substitution "x", "y", .3,-.2, 4, .4, .5, -29/19 ]


Same result as before.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J