Question 449108
1. {{{(1/5)x + (1/5)y = 1}}}
2. {{{(1/5)x - (1/5)y = 9/5}}}
==> Clear fractions by multiplying all elements by 5 (the LCD):
1. {{{(5)(1/5)x + (5)(1/5)y = (5)(1)}}}
2. {{{(5)(1/5)x - (5)(1/5)y = (5)(9/5)}}}
==> Simplify. Notice that (5) cancels out (/5):
1. {{{x + y = 5}}}
2. {{{x - y = 9}}}
==> Since you want to solve by substitution, you must isolate any variable in either of the equations. I am going to isolate the x in the second equation by adding y to both sides.
2. {{{x = y + 9}}}
==> Substitute this value (y + 9) for x into the first equation.
1. {{{y + 9 + y = 5}}}
==> Add like terms:
1. {{{2y + 9 = 5}}}
==> Subtract 9 from both sides:
1. {{{2y = -4}}}
==> Divide both sides by 2:
1. {{{y = -2}}}
==> So, your y-coordinate is -2. Next, solve for x by plugging this value of y into the equation for x found a few steps ago (x = y + 9):
{{{x = -2 + 9}}}
==> Add like terms:
{{{x = 7}}}
==> So, x-coordinate is 7. Plug these values for x and y into coordinate form (x, y): (7, -2)
***Therefore, your answer is (7, -2)