A mixture of dimes and quarters has a total value of $10.20. There are 57 coins in all. How many type of each coin is present?
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Answer:
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The solution for the system equations is (2 , 0 , -2).
<h3>System of Equations</h3>
A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other. To solve this question, you will apply the addition method.
The question gives three equations:
(1) 4x−2y+z=6
(2) −2x+y=−4
(3) 3y−2z=4
You should isolate the variable x in equation (2), then you will have
. After that, you should use this variable in equation (1), see below
Equation 1 (4x−2y+z=6)
If z=-2, from equation (3), you find y, see below.
3y-2z=4
3y-2*(-2)=4
3y+4=4
3y=4-4
3y=0
y=0
If y=0, from equation (2), you find x, see below.
−2x+y=−4
-2x+0=-4
-2x=-4
x=2
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