Michael J. answered • 11/20/16
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Effective High School STEM Tutor & CUNY Math Peer Leader
Let the cost of one bar of soap = x
Let the cost of one tube of toothpaste = y
Use these variables to create a system of equations.
3x + 2y = 4.05 eq1 ---> total cost of one set
2x + 3y = 5.20 eq2 ---> total cost of second set
Solve the system of equations for x and y using substitution/elimination methods.
Michael J.
In some cases, we can use the substitution method to substitute one equation into another equation. This only works if any one of the equations a coefficient of 1 for x or variable.
Since we are not in that case, we must use the elimination method. This method allows us to add or subtract equations with like terms in order to eliminate a variable. If the equations do not have like terms, then we multiply the equations so that we get like terms.
For example, if we multiply eq1 by 3 and eq2 by 2, we get equations with like terms.
9x + 6y = 12.15 eq1
4x + 6y = 11.40 eq2
Notice that both equations have a 6y term in common. If we subtract eq2 from eq1, we can eliminate the y terms. You end up with an equation such that
3x = 0.75
Now you can solve for x. Then substitute that value of x into the other equation to solve for y.
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11/20/16
Michael J.
*Substitution only works if any one of the equations have a coefficient of 1 for x or y variable.
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11/20/16
Kim B.
11/20/16