How do you solve the following system: 2x+7y=1, 5x - 7y = 12 ?

1 Answer
Aug 13, 2017

See a solution process below:

Explanation:

Step 1) Solve each equation for 7y:

Equation 1:

2x + 7y = 1

-color(red)(2x) + 2x + 7y = -color(red)(2x) + 1

0 + 7y = -2x + 1

7y = -2x + 1

Equation 2:

5x - 7y = 12

-color(red)(5x) + 5x - 7y = -color(red)(5x) + 12

0 - 7y = -5x + 12

-7y = -5x + 12

color(red)(-1) xx -7y = color(red)(-1)(-5x + 12)

7y = 5x - 12

Step 2) Because the left side of each equation is 7y we can equate the right side of each equation and solve for x:

-2x + 1 = 5x - 12

color(red)(2x) - 2x + 1 + color(blue)(12) = color(red)(2x) + 5x - 12 + color(blue)(12)

0 + 13 = (color(red)(2) + 5)x - 0

13 = 7x

13/color(red)(7) = (7x)/color(red)(7)

13/7 = (color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7))

13/7 = x

x = 13/7

*Step 3) Substitute 13/7 for x in the solution to either equation in Step 1 and calculate y:

7y = -2x + 1 becomes:

7y = (-2 xx 13/7) + 1

7y = -26/7 + 1

7y = -26/7 + (7/7 xx 1)

7y = -26/7 + 7/7

7y = -19/7

(7y)/color(red)(7) = (-19/7)/color(red)(7)

(color(red)(cancel(color(black)(7)))y)/cancel(color(red)(7)) = -19/49

y = -19/49

The Solution Is: x = 13/7 and y = -19/49 or (13/7, -19/49)