SOLUTION: 1.) Solve the system. 4x + 3y = 11 3x - 2y= 4 2.) Is this right?: Jennifer has collected $4.50 in nickels and dimes. If she has 55 coins, how many of each kind of coin does sh

Question 125447: 1.) Solve the system.
4x + 3y = 11
3x - 2y= 4
2.) Is this right?: Jennifer has collected $4.50 in nickels and dimes. If she has 55 coins, how many of each kind of coin does she have? Answer: 35 dimes and 20 nickles.
3.) Solve the following linear inequality graphically.
x+ 2y <4
x - y <5
I've solved #2, hopefully it is right. Any help with checking that one and helping with the others would be highly appreciated.
Thanks!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1.) Solve the system.
4x + 3y = 11
3x - 2y= 4
-----------------
Multiply 1st by 2 and 2nd by 3 to get :
8x + 6y = 22
9x - 6y = 12
-----------------
Add the two equations and solve for "x":
17x = 34
x = 2
-----------
Substitute in one of the original equations to solve for "Y".
4*2 + 3y = 11
3y = 3
y = 1
============================
2.) Is this right?: Jennifer has collected $4.50 in nickels and dimes. If she has 55 coins, how many of each kind of coin does she have? Answer: 35 dimes and 20 nickles.
Correct because 35*10 cents + 20 * 5 cents = 450 cents
-------------------------
3.) Solve the following linear inequality graphically.
x+ 2y <4
x - y <5
------------
Solve both equtions for y to get:
y < (-1/2)x + 2
y >x - 5
--------------
Graph the boundary of each of the inequalities as dashed lines:

----------------
Shade or "hatch" the half-plane below the 1st boundary because
of the "<" sign on the inequality.
Shade or "hatch" the half-plane above the 2nd boundary because
of the the ">" sign on the inequality.
--------------------
The solution set is the intersection of the two half-planes.
========================
Cheers,
Stan H.

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