Answer: (6, -1)
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Explanation:
If you were to multiply both sides of the second equation by 4, then,
[tex]\frac{1}{2}x-5y = 8\\\\4\left(\frac{1}{2}x-5y\right) = 4*8\\\\2x-20y = 32\\\\[/tex]
The original system of equations is equivalent to this system
[tex]\begin{cases}2x+y = 11\\2x-20y = 32\end{cases}[/tex]
Let's subtract straight down.
- The x terms have the same coefficient (2) out front. This means when we subtract the x terms, they'll go away. 2x-2x = 0x = 0.
- Subtracting the y terms gets us: y-(-20y) = y+20y = 21y
- Subtracting the right hand sides gets us: 11-32 = -21
After those three sets of subtractions are performed, we have this new equation: [tex]21 y = -21[/tex] and that solves to [tex]y = -1[/tex] (divide both sides by 21).
Now use this y value to find x. You can pick any equation with x & y in it.
[tex]2x+y = 11\\\\2x+(-1) = 11\\\\2x-1 = 11\\\\2x = 11+1\\\\2x = 12\\\\x = 12/2\\\\x = 6[/tex]
The solution as an ordered pair is (x,y) = (6, -1)
The two lines cross at this location.
