How do you solve the system of equations #-16x - 4y = 12# and #- 4x + y = - 11#?

Question

Avery Alexander · Accepted Answer

#x=1 and y=-7#

Given 2 equations, let us number them

#-16x-4y=12 # we can simplify this equation by 4 , it would be easier for solving

#rArr(-16x-4y)/4=12/4# #rArrcolor(blue)(-4x-y=3# equation1

the two equations are:

#color(blue)(-4x-y=3)# #color(red)(-4x+y=-11)#

First we add both equations : #color(blue)(-4x-y)color(red)(-4x+y)=3-11# #-8x+0y=-8# #-8x=-8# #x=-8/-8# #color(green)(x=1)#

second, let us substitute the value of #x# in equation 2 #color(red)(-4*1+y=-11)# #rArr-4+y=-11# #rArry=-11+4# #color(green)(y=-7)#

Third, check if the values #color(green)(x=1 and color(green)(y=-7)# by substituting it in equation 1 #color(blue)(-4x-y=3)# #color(blue)(-4(color(green)1)-(color(green)(-7))=?3)# #color(blue)(-4+7=?3)# #-3=?-3 true#

therefore,x=1 and y=-7#

Kennedy Adams · Answer

undefined To solve the system of equations $ -16x - 4y = 12 $ and $ -4x + y = -11 $, you can use the method of substitution or elimination. Let's use the substitution method here:

First, solve the second equation for y:
$$ -4x + y = -11 $$
$$ y = -11 + 4x $$

Now substitute this value of y into the first equation:
$$ -16x - 4(-11 + 4x) = 12 $$
$$ -16x + 44 - 16x = 12 $$

Combine like terms:
$$ -32x + 44 = 12 $$

Subtract 44 from both sides:
$$ -32x = -32 $$

Divide by -32:
$$ x = 1 $$

Now substitute the value of x back into the second equation to find y:
$$ y = -11 + 4(1) $$
$$ y = -11 + 4 $$
$$ y = -7 $$

So the solution to the system of equations is $ x = 1 $ and $ y = -7 $.