Question

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Answer 1

Answer:   (6, -1)

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Explanation:

If you were to multiply both sides of the second equation by 4, then,

$\frac{1}{2}x-5y = 8\\\\4\left(\frac{1}{2}x-5y\right) = 4*8\\\\2x-20y = 32$

The original system of equations is equivalent to this system

$\begin{cases}2x+y = 11\\2x-20y = 32\end{cases}$

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: $21 y = -21$ and that solves to $y = -1$ (divide both sides by 21).

Now use this y value to find x. You can pick any equation with x & y in it.

$2x+y = 11\\\\2x+(-1) = 11\\\\2x-1 = 11\\\\2x = 11+1\\\\2x = 12\\\\x = 12/2\\\\x = 6$

The solution as an ordered pair is (x,y) = (6, -1)

The two lines cross at this location.