Final answer:
The value of 2x+17y is 5.1818.
Step-by-step explanation:
To find the value of 2x+17y, we first need to solve the given system of equations:
Equation 1: 3x+10y=2
Equation 2: -x+7y=-4
Multiplying Equation 1 by 2, we get: 6x+20y=4
Adding this new equation to Equation 2, we can eliminate the x variable:
6x+20y-x+7y=4-4
Simplifying, we get: 5x+27y=0
Now we have a new system of equations:
Equation 3: 5x+27y=0
Equation 2: -x+7y=-4
Multiplying Equation 2 by 5 and Equation 3 by 7, we get:
Equation 4: -5x+35y=-20
Equation 5: 35x+189y=0
Adding Equations 4 and 5, we can eliminate the x variable:
-5x+35y+35x+189y=-20+0
Simplifying, we get: 224y=-20
Dividing both sides by 224, we find: y=-20/224=-1/11
Substituting this value of y into Equation 2 to solve for x: -x+7(-1/11)=-4
Simplifying, we get: -x-7/11=-4
Adding 7/11 to both sides, we find: -x=-4+7/11
Simplifying, we get: -x=-37/11
Dividing both sides by -1, we find: x=37/11
Now that we have the values of x and y, we can calculate 2x+17y:
2(37/11)+17(-1/11) = 74/11 - 17/11 = 57/11 = 5.1818 (rounded to 4 decimal places)