jessica and castel each improved their yards by planting daylilies and ornamental grass. they bought their supplies from the same store. jessica spent $47 dollars on 2 daylillies and 3 bunches of ornamental grass. Castel spent $87 on 6 daylilies and 3 bunches of ornamental grass. find the cost of one daylily and the cost of one bunch of ornamental grass.
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This is two equations two variables. Let x be the cost of 1 bunch daylillies and y be the cost of 1 bunch of ornamental grass.
So 2x + 3y = 47 and 6x + 3y = 87
Do you understand so far?
Put those on top of each other (one above the other)
The idea is to get rid of one of the letters. so we should have a 3y over a 3y. If the bottom one was -3y we could add them up and they would go away.
So. let's change the sign of every term on the bottom.
2x + 3y = 47
-6x - 3y = -87
OK so far?
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So add straight down and you get -4x = -40
Divide both sides by -4 and you get
x = 10
Plug that into one of the equations and solve for y
2x + 3y = 47
2(10) + 3y = 47
20 + 3y = 47 subtract 20 from both sides
3y = 27 divide both sides by 3
y = 9
So the cost of one daylilly was $10 (because x = 10)
The cost of one ornamental was $9 (because y = 9)