You are planning to purchase ten pencils of type A which cost a total of $14.00 and five pencils of type B which cost $15.00. A)
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Answer:
The value of the variable x is -2 and the value of the variable y is -7.
Step-by-step explanation:
The substitution method consists of:
- Solve for an unknown in one of the equations, which will be a function of the other unknown .
- In the other equation that is not used, the same unknown is replaced by the expression obtained in step 1.
- Solve for the only remaining unknown, obtaining the numerical value of an unknown.
- Substitute the cleared unknown in step 3 for its numerical value in the equation obtained in step 1.
- Operate to obtain the numerical value of the other unknown.
In this case, you have the system of equations:
Isolating the variable y from the second equation:
y= -1 +3*x
Replacing this expression in the first equation:
2*x-3*( -1 +3*x)= 17
Solving:
2*x -3*(-1)-3*3*x= 17
2*x +3 -9*x= 17
2*x -9*x= 17 -3
(-7)*x= 14
x= 14÷(-7)
x= -2
Now, replacing the value of x in the expression y = -1 + 3 * x you get:
y= -1 +3*(-2)
Solving:
y= -1 -6
y= -7
So,<u><em> the value of the variable x is -2 and the value of the variable y is -7.</em></u>