What is yy and xx when y= 2x-11y=2x−11 and y= x- 8y=x−8 ?

2 Answers
David Drayer
Apr 5, 2017

x = + 3 y = -5

Explanation:

One way to solve the problem is to subtract the two equations from each other.

y = 2x - 11 - (y = x - 8 )y=2x−11−(y=x−8)

y-y = 0y−y=0
2x - x = x2x−x=x
- 11 -( -8) = -3−11−(−8)=−3

so y = 2x - 11 - ( y = x -8) = { 0 = x - 3}y=2x−11−(y=x−8)={0=x−3}

Solving for 0 = x -30=x−3 add 3 to both sides giving

0 + 3 = x -3 + 30+3=x−3+3 so

+3 = x +3=x

now put the value of +3 into either equation and solve for y

y = +3 -8y=+3−8

y = -5y=−5

To check put these values into the second equation

-5 = 2(+3) - 11−5=2(+3)−11

-5 = +6 -11−5=+6−11

# -5 = -5 check

x = +3 y = -5

Barney V.
Apr 5, 2017

color(red)(y=-5,x=3y=−5,x=3

Explanation:

y=2x-11y=2x−11 ------(1)

y=x-8y=x−8 ---------(2)

(2) xx 2(2)×2

2y=2x-162y=2x−16 ------(3)

(1)-(3)(1)−(3)

-y=5−y=5

color(red)(y=-5y=−5

substitute color(red)(y=-5y=−5 in (2)

color(red)(-5)=x-8−5=x−8

x-8=-5x−8=−5

x=-5+8x=−5+8

color(red)(x=3x=3

substitute color(red)(y=-5,x=3y=−5,x=3 in (1)

color(red)(-5)=2(color(red)3)-11−5=2(3)−11

-5=6-11−5=6−11

-5=-5−5=−5

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