How can we solve the following system of equations: 2y = 6 and 2x + 4y = 10?

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To solve the system of equations 2y = 6 and 2x + 4y = 10, we can use substitution or elimination methods. Here, we’ll outline the substitution method.

Step 1: Solve for y

First, simplify the first equation to find the value of y:

2y = 6
=> y = 6 / 2
=> y = 3

Step 2: Substitute y into the second equation

Now that we have the value of y, we can substitute it into the second equation:

2x + 4y = 10
=> 2x + 4(3) = 10

Now, simplify it:

2x + 12 = 10

Step 3: Solve for x

Next, isolate x:

2x = 10 - 12
=> 2x = -2
=> x = -2 / 2
=> x = -1

Final Solution

Thus, the solution to the system of equations is:

  • x = -1
  • y = 3

In summary, the solution is the ordered pair (-1, 3).

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