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If 3x+10y=2 and -x+7y=-4 are true equations, what would be the value of 2x+17y

User SPIELER
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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)

User Silda
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