Answer:
Step-by-step explanation:
given system :
y=-2x+6 ........(1)
3y-x+3=23.........(2)
Substitute y = -2x+6 into (2) and solve for x :
3( -2x+6) - x +3 = 23
- 6x +18 - x +3 =23
- 7x = 2
x =- 2/7
Substitute : x into (1) : y = -2 (-2/7)+6 = 46/7
2x-1+3 < 6
+1 < +1
2x+3 < 7
-3 < -3
2x < 4
/2 < /2
x < 2
Answer:
$300
Step-by-step explanation:
Let Dave's saving be D and Sam's savings be S
- <u>"At first, the ratio of Dave's savings to Sam's savings was 5:4":</u>
![\frac{D}{S}=\frac{5}{4}\\4D=5S\\\frac{4}{5}D=S](https://tex.z-dn.net/?f=%5Cfrac%7BD%7D%7BS%7D%3D%5Cfrac%7B5%7D%7B4%7D%5C%5C4D%3D5S%5C%5C%5Cfrac%7B4%7D%7B5%7DD%3DS)
- <u>"After each of them donated $40 to charity, the ratio of Dave's savings to Sam's savings became 13:10":</u>
<em>So we subtract 40 from each of them and then the ratio becomes 13 is to 10. Hence we can write:</em>
![\frac{D-40}{S-40}=\frac{13}{10}\\10(D-40)=13(S-40)\\10D-400=13S-520\\-400+520=13S-10D\\120=13S-10D](https://tex.z-dn.net/?f=%5Cfrac%7BD-40%7D%7BS-40%7D%3D%5Cfrac%7B13%7D%7B10%7D%5C%5C10%28D-40%29%3D13%28S-40%29%5C%5C10D-400%3D13S-520%5C%5C-400%2B520%3D13S-10D%5C%5C120%3D13S-10D)
<em>Plugging in
into S (as we found earlier), we can solve for D (our answer):</em>
![120=13S-10D\\120=13(\frac{4}{5}D)-10D\\120=\frac{52}{5}D-10D\\120=\frac{2}{5}D\\D=\frac{120}{\frac{2}{5}}=120*\frac{5}{2}=300](https://tex.z-dn.net/?f=120%3D13S-10D%5C%5C120%3D13%28%5Cfrac%7B4%7D%7B5%7DD%29-10D%5C%5C120%3D%5Cfrac%7B52%7D%7B5%7DD-10D%5C%5C120%3D%5Cfrac%7B2%7D%7B5%7DD%5C%5CD%3D%5Cfrac%7B120%7D%7B%5Cfrac%7B2%7D%7B5%7D%7D%3D120%2A%5Cfrac%7B5%7D%7B2%7D%3D300)
So, Dave's savings at first, D, is $300.