SOLUTION: Solve the following 2 x 2 systems using substitutions 2x - 5y= 21 7x + 3y = 53

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Question 72335: Solve the following 2 x 2 systems using substitutions
2x - 5y= 21
7x + 3y = 53
Answer by elima(1433) About Me  (Show Source):
You can put this solution on YOUR website!
2x - 5y= 21
7x + 3y = 53
Lets start with changing the first equation to x equals;
2x=21+5y
x=21%2F2+5y%2F2
now replace the x in the second equation;
7(21%2F2+5y%2F2)+3y=53
Distribute the 7;
147%2F2+35y%2F2+3y=53
subtract 147%2F2from both sides and add like terms;
35y%2F2+3y=53-147%2F2
get common denominators so you can add or subtract fractions;
35y%2F2+6y%2F2=106%2F2-147%2F2
41%2F2y=-41%2F2
multiply each side by the reciprocal of 41%2F2;
(2%2F41)41%2F2y=-41%2F2(2%2F41)
y=-82%2F82=-1
Now replace the y in the first equation with -1;
2x - 5(-1)= 21
2x+5=21
2x=16
x=8
so answer; y=-1, x=8
:)