Solve the system of equations.

Question

Solve the system of equations.

2x + 8y = 8

2x - 4y = - 16 (1 point)

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3 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

To solve the system of equations, we can use the method of substitution or elimination. In this case, let's use the method of elimination.

First, we'll multiply the second equation by -1 to make the coefficients of x the same.

Original equations:
2x + 8y = 8
2x - 4y = - 16

Modified equations:
2x + 8y = 8
-2x + 4y = 16

Now, let's add the two equations together to eliminate x:
(2x + 8y) + (-2x + 4y) = 8 + 16
12y = 24
y = 2

Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

2x + 8(2) = 8
2x + 16 = 8
2x = -8
x = -4

So the solution to the system of equations is x = -4 and y = 2.

Answer 2

Step-by-Step Bot answered
1 year ago

To solve the system of equations, we can use the method of elimination.

Step 1: Multiply both sides of the second equation by -1 to change the sign:

-1(2x - 4y) = -1(-16)
-2x + 4y = 16

Step 2: Now we have the following system of equations:
2x + 8y = 8
-2x + 4y = 16

Step 3: Add the two equations together to eliminate the x variable:
(2x + 8y) + (-2x + 4y) = 8 + 16
2y = 24
y = 12

Step 4: Substitute the value of y = 12 into one of the original equations to solve for x. Let's use the first equation:
2x + 8y = 8
2x + 8(12) = 8
2x + 96 = 8
2x = -88
x = -44

Therefore, the solution to the system of equations is x = -44 and y = 12.

Answer 3

Explain Bot answered
1 year ago

To solve this system of equations, we can use the method of elimination. The goal is to eliminate one variable by manipulating one or both of the equations so that when we add or subtract them, one variable cancels out.

Let's start by subtracting the second equation from the first equation:

(2x + 8y) - (2x - 4y) = 8 - (-16)

Simplifying both sides of the equation, we get:

2x + 8y - 2x + 4y = 8 + 16

Combining like terms, we have:

12y = 24

Now, we can solve for y by dividing both sides of the equation by 12:

12y/12 = 24/12

Simplifying, we get:

y = 2

Now that we know the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

2x + 8(2) = 8

Simplifying, we have:

2x + 16 = 8

Subtracting 16 from both sides of the equation gives us:

2x = -8

Finally, we can solve for x by dividing both sides of the equation by 2:

2x/2 = -8/2

Simplifying further, we find:

x = -4

Therefore, the solution to the system of equations is x = -4 and y = 2.