Question 1196487
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x = cost of 1 scone
y = cost of 1 coffee
Prices are in dollars


7x = cost of 7 scones
2y = cost of 2 coffees
7x+2y = total cost
7x+2y = 22.80


Follow similar steps to get the other equation of 4x+3y = 16.52


We have this system of equations
7x+2y = 22.80
4x+3y = 16.52


Let's say we wanted to eliminate the y terms
Triple both sides of equation (1) and double both sides of equation (2)
We'll end up with this equivalent system
21x+6y = 68.40
8x+6y = 33.04
The goal is to have the y terms match (ie both coefficients are 6)


Now subtract straight down<ul><li>The x terms subtract to 21x-8x = 13x</li><li>The y terms subtract to 6y-6y = 0y = 0, so they cancel out.</li><li>The right hand sides subtract to 68.40-33.04 = 35.36</li></ul>After the y terms cancel, we have: 13x = 13.56
That solves to x = 2.72 after dividing both sides by 13


Let's find the value of y based on that x value
Pick any previously mentioned equation involving x and y
Plug in x = 2.72 and solve for y
7x+2y = 22.80
7(2.72)+2y = 22.80
19.04+2y = 22.80
2y = 22.80-19.04
2y = 3.76
y = 3.76/2
y = 1.88


Answer:
Price of one scone = $2.72
Price of one coffee = $1.88
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