Solve by Substitution x+14y=2 , 2x+7y=-8

Problem

{[x+14*y=2],[2*x+7*y=−8])

Solution

1. Isolate the variable x in the first equation by subtracting 14*y from both sides.

x=2−14*y

2. Substitute the expression for x into the second equation.

2*(2−14*y)+7*y=−8

3. Distribute the 2 into the parentheses.

4−28*y+7*y=−8

4. Combine the y terms.

4−21*y=−8

5. Isolate the y term by subtracting 4 from both sides.

−21*y=−12

6. Solve for y by dividing both sides by −21 and simplifying the fraction.

y=(−12)/(−21)

y=4/7

7. Substitute the value of y back into the isolated expression for x

x=2−14*(4/7)

8. Simplify the expression to find the value of x

x=2−2*(4)

x=2−8

x=−6

Final Answer

(x,y)=(−6,4/7)

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