Question 1208685
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x = sofa's price
y = love seat's price
z = chair's price
Each price is in dollars.


The various combo prices in the instructions gives us this system of equations.
{{{system(x+y = 1300,x+2z=1400,x+y+z=1600)}}}
Since x+y = 1300, we can replace the x+y in the 3rd equation with 1300
So,
x+y+z = 1600
<font color=blue>x+y</font>+z = 1600
<font color=blue>1300</font>+z = 1600
z = 1600-1300
z = <font color=red>300</font>
Put another way: subtract equations (3) and (1) to end up with z = 300.


Use this value of z to find x in the 2nd equation
x+2z = 1400
x+2*300 = 1400
x+600 = 1400
x = 1400-600
x = <font color=red>800</font>


Then use the 1st equation to find y.
x+y = 1300
800+y = 1300
y = 1300-800
y = <font color=red>500</font>



Answers:
Sofa = <font color=red>$800</font>
Love Seat = <font color=red>$500</font>
Chair = <font color=red>$300</font>
I'll let the student check these answers.
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