2/3x + y = 14/3
4/5x - 3/4y = -10
the first step in solving this system of equations by elimination is to match the coefficients of one of your variables. since "y" in your first equation has no coefficients, it'll be easiest to multiply the top equation by (-3/4) to get your coefficients equal.
(2/3x + y = 14/3) * (-3/4)
4/5x - 3/4y = -10
leave the second equation alone for now. distribute the (-3/4) into the parentheses. remember that to use elimination, you have to line the equations up and subtract them:
-1/2x - 3/4y = -7/2
- (4/5x - 3/4y = -10)
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-13/10x = 13/2 .... divide both sides by (-13/10). remember, to divide a fraction by a fraction, you flip the second fraction and multiply through.
x = -5 is your result.
now that you have one variable, plug it back into one of your equations. the second equation will do just fine:
4/5(-5) - 3/4y = -10 ... your 5s cancel out
-4 - 3/4y = -10 ... add 4
-3/4y = -6 ... divide both sides by (-3/4)
y = 8 is your result.
the ordered pair representing the solution to this equation would be (-5, 8).
