Sure! Let's solve the system of equations step by step.
We are given the system of equations:
1. [tex]\( y = 3x - 12 \)[/tex]
2. [tex]\( 4x + 6y = -6 \)[/tex]
First, we will substitute the expression for [tex]\( y \)[/tex] from the first equation into the second equation.
Given [tex]\( y = 3x - 12 \)[/tex], substitute into the second equation:
[tex]\[ 4x + 6(3x - 12) = -6 \][/tex]
Now, let's simplify and solve for [tex]\( x \)[/tex].
1. Distribute the 6:
[tex]\[ 4x + 18x - 72 = -6 \][/tex]
2. Combine like terms:
[tex]\[ 22x - 72 = -6 \][/tex]
3. Add 72 to both sides of the equation:
[tex]\[ 22x = 66 \][/tex]
4. Divide both sides by 22:
[tex]\[ x = 3 \][/tex]
Now that we have [tex]\( x = 3 \)[/tex], we substitute this back into the first equation to find [tex]\( y \)[/tex]:
[tex]\[ y = 3(3) - 12 \][/tex]
[tex]\[ y = 9 - 12 \][/tex]
[tex]\[ y = -3 \][/tex]
So, the solution to the system of equations is [tex]\( (x, y) = (3, -3) \)[/tex].
Therefore, the ordered pair that is the solution to the system of equations is [tex]\( (3, -3) \)[/tex].
