What is the solution to the system of equations below

What is the solution to the system of equations below?
x + 3 y = 15 and 4 x + 2 y = 30
(6, 3)
(3, 6)
(7, –6)
(–6, 7)

The Correct Answer and Explanation is :

The correct answer is: (6, 3).

To solve the system of equations given by:

1. ( x + 3y = 15 ) (Equation 1)
2. ( 4x + 2y = 30 ) (Equation 2)

we can use the substitution or elimination method. Here, I’ll demonstrate the elimination method.

First, we can manipulate Equation 1 to express one variable in terms of the other. Let’s solve for ( x ) in terms of ( y ):

[
x = 15 – 3y \tag{Equation 3}
]

Next, we can substitute Equation 3 into Equation 2:

[
4(15 – 3y) + 2y = 30
]

Now, distribute ( 4 ):

[
60 – 12y + 2y = 30
]

Combine like terms:

[
60 – 10y = 30
]

Now, isolate ( y ) by subtracting ( 60 ) from both sides:

[
-10y = 30 – 60
]
[
-10y = -30
]

Now, divide both sides by ( -10 ):

[
y = 3
]

Next, substitute ( y = 3 ) back into Equation 3 to find ( x ):

[
x = 15 – 3(3)
]
[
x = 15 – 9
]
[
x = 6
]

Thus, the solution to the system of equations is ( (6, 3) ).

To verify, we can substitute ( x = 6 ) and ( y = 3 ) back into both original equations:

1. For Equation 1:
   [
   6 + 3(3) = 6 + 9 = 15 \quad \text{(True)}
   ]
2. For Equation 2:
   [
   4(6) + 2(3) = 24 + 6 = 30 \quad \text{(True)}
   ]

Since both equations are satisfied, the solution ( (6, 3) ) is correct. Thus, the answer to the system of equations is (6, 3).