Question

Find the value of x and yD%201" id="TexFormula1" title="2x + 5y = - 5 \\ - 8x - 1y = 1" alt="2x + 5y = - 5 \\ - 8x - 1y = 1" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

(x,y)=(0,-1)

Step-by-step explanation:

Answer 2

Answer:  x = 0  y = -1

Step-by-step explanation:

To solve by elimination, multiply the first  equation by 4 , then add the two equations

(4)(2x + 5y = -5) becomes

8x +20y = -20

-8x  -1y   =  1     becomes

  0 + 19y = -19  divide both sides by 19

  y = -1   Substitute -1 for y in either equation, then solve for x

2x + 5( -1) = -5    Distribute

 2x  -5 = -5  Add 5 to both sides

2x +5 -5 = -5 + 5  Combine like terms.

 2x = 0  

Check: 2x + 5y = -5  is  2(0) = 5(-1) = -5

0 + -5 = -5  True  

 -8x  -1y   =  1  is  -8(0) -1(-1) = 1    

 0 + 1 = 1    True

OR

To solve by substitution, rewrite the second equation to isolate y.

-8x -1y = 1  Add 8x to both sides

-1y = 8x + 1 Multiply both sides by -1

y = -8x -1 Substitute (-8x -1) in place of y in the first equation.

2x + 5y = -5 becomes

2x + 5(-8x -1) = -5 Distribute and rewrite

2x - 40x -5 = -5   Add 5 to both sides

2x - 40x -5 = -5 + 5 Combine like terms.

-38x = 0  To Solve for x, Divide both sides by -38   (Actually unnecessary!)

x = 0  Substitute this value for x in the second equation and solve for y

-8(0) -1y = 1

0 - y = 1

-y = 1 Multiply both sides by -1 (reverse signs)

y = -1