How do you solve the following system?: # -2x +5y =-6 , 5x +6y = -1#

Question

How do you solve the following system?: # -2x +5y =-6 ,  5x +6y = -1#

Kennedy Adams · Accepted Answer

#x = 31/37, y = -32/37#

We can solve for #y# first by multiplying the first equation by #5# and the second equation by #2#:

#5(-2x + 5y) = (-6)5# and #2(5x + 6y) = (-1)2#

The two equations are then added, giving rise to:

#25y + 12y = -32#, and therefore, #37y = -32#

We divide both sides by #37#, so #y = -32/37#

To solve for #x#, we multiply the first equation by #-6# and the second equation by #5#:

#-6(-2x + 5y) = -6(-6)# and #5(5x + 6y) = 5(-1)#

The two equations are then added, giving rise to:

#12x + 25x = 31#, and therefore, #37x = 31#

We divide both sides by #37#, so #x = 31/37#

You can verify these answers by substituting #31/37# for #x# and #-32/37# for #y#:

#-2(31/37) + 5(-32/37) = -62/37 - 160/37 = -222/37 = -6#

Genesis Allen · Answer

undefined To solve the system of equations:

$$ -2x + 5y = -6 $$
$$ 5x + 6y = -1 $$

You can use the method of substitution or elimination. Let's use the elimination method:

1. Multiply the first equation by 5 and the second equation by 2 to make the coefficients of $ x $ equal and opposite:
$$ -10x + 25y = -30 $$
$$ 10x + 12y = -2 $$

2. Add the equations together:
$$ ( -10x + 25y) + (10x + 12y) = (-30) + (-2) $$
$$ 37y = -32 $$

3. Solve for $ y $:
$$ y = \frac{-32}{37} $$

4. Substitute $ y $ back into one of the original equations to solve for $ x $. Let's use the first equation:
$$ -2x + 5(\frac{-32}{37}) = -6 $$

5. Solve for $ x $:
$$ x = \frac{49}{37} $$

So, the solution to the system of equations is $ x = \frac{49}{37} $ and $ y = \frac{-32}{37} $.