Solve the following system by elimination. (x-1)/(2) + (y+2)/(3) = 4 x - 2y = 5

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Given the system `(x-1)/2+(y+2)/3=4` and `x-2y=5` .

(1) Lets put the first equation in standard form:

`(x-1)/2+(y+2)/3=4` Given

`3(x-1)+2(y+2)=24` Multiply both sides by 6 to clear fractions

`3x+2y=23` Distribute then collect like terms

(2) Now the system is:

`x-2y=5` Add the two equations:

`4x=28 =>x=7` . Plugging x=7 into an original equation yields y=1.

Checking we have `(7-1)/2+(1+2)/3=4` and `7-2(1)=5` .

So the solution is (7,1).