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3 years ago

What is the solution set of the system {2x - 3y =19 and 7x +4y = -6?

1 answer:

6 0

{ 2x-3y=19
{ 7x+4y=-6

{ 2x=19+3y
{ 7x=-6-4y

{ x=19/2+3/2y
{ x=-6/7-4/7y

19/2+3/2y=-6/7-4/7y
y=-5

x=-6/7-4/7(-5)
x=2

(x,y) = (2,-5)

Solution Check
{ 2 · 2-3(-5)=19
{ 7 · 2+4(-5)=-6

{ 19=19
{ -6=-6

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2 years ago

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2 years ago

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Answer A: 35 dimes and 5 nickels

Step-by-step explanation:

Let say

d the number of dimes

n the number of nickels

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Total value : 0.1*d+0.05n=2.25

$\left\{\begin {array} {ccc}d+n&=&40\\10*d+5*n&=&225\ multiplied\ by\ 100\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}n&=&40-d\\10*d+5*(40-d)&=&225\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}5*d&=&225-200\\n&=&40-d\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}5*d&=&25\\n&=&40-5\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}d&=&5\\n&=&35\\\end {array}\right.\\\\Proof:\\5*0.1+35*0.05=0.5+1.75=2.25\\$

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