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Solve the following system of equations by substitution
x-4y=-1
3x+5y = 31

User Dwayne
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1 Answer

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Final answer:

The solution to the system of equations is found by isolating x in the first equation, substituting it into the second equation, and solving for y. Then y is substituted back into the first equation to find x, resulting in x = 3.4706 and y = 4.1176.

Step-by-step explanation:

To solve the given system of equations by substitution, let's start by isolating x in the first equation.

1. Given the first equation x - 4y = -13, we can solve for x:

x = 4y - 13

2. We now substitute x into the second equation:

3x + 5y = 31 becomes:

3(4y - 13) + 5y = 31

3. Expanding and simplifying the equation we get:

12y - 39 + 5y = 31

17y - 39 = 31

4. Adding 39 to both sides gives us:

17y = 70

5. Dividing both sides by 17 we find the value of y:

y = 70 / 17

y = 4.1176

6. Substitute y back into the equation x = 4y - 13 to find x:

x = 4(4.1176) - 13

x = 16.4706 - 13

x = 3.4706

So the solution to the system of equations is x = 3.4706 and y = 4.1176.

User Suzon
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