How do you find the solution of the system of equations -4x=y+1−4x=y+1 and -8x-5y=-19−8x−5y=−19?

2 Answers
Jeremiah Kevin M.
Jun 17, 2018

We solve these kind of equation simultaneously...

-4x=y+1−4x=y+1
or, y=-1-4xy=−1−4x...................i

And,
The other equation is :
-8x-5y=-19−8x−5y=−19......ii

Now put the value of yy (which is -1-4x−1−4x) in the second equation:
-8x-5(-1-4x)=-19−8x−5(−1−4x)=−19

or, -8x+5+20x=-19−8x+5+20x=−19

or, 12x=-2412x=−24

Thus x=-2x=−2

And now we have the values o xx so let's put it in the first equation:
y=-1-4xy=−1−4x
y=-1+8y=−1+8
Thus, y=7y=7

HUSHTeacher · Stefan V.
Jun 17, 2018

Substitution is the easiest way to complete this problem.

Explanation:

-4x = y + 1" " " " (1)−4x=y+1 (1)
-8x - 5y = -19 " " " " (2)−8x−5y=−19 (2)

(1)(1)

Subtract the 11 on both sides:

-4x - 1 = y−4x−1=y

Replace the yy in the second equation with -4x - 1−4x−1

(2)

-8x - 5(-4x - 1) = -19−8x−5(−4x−1)=−19

Distribute the -5−5 into the parentheses

-8x + 20x + 5 = -19−8x+20x+5=−19

Add -8x−8x and 20x20x

12x + 5 = -1912x+5=−19

Subtract the 55 on both sides

12x = -2412x=−24

Divide by 1212 on both sides

x = -2x=−2

To find the yy value, substitute the xx value into one of the original equations:

(1)(1)

-4(-2) = y + 1−4(−2)=y+1

Multiply -4−4 and -2−2

8 = y + 18=y+1

Subtract the 11 on both sides

7 = y7=y

Answer:

(-2 , 7)(−2,7)

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