Answer:
[tex]\sf x = -12 [/tex] and [tex]\sf y = -21 [/tex]
Step-by-step explanation:
To solve this system of linear equations, we'll use the method of substitution or elimination. Let's use the substitution method:
Given the system of equations:
[tex] \begin{cases} \sf y = 2x + 3 \\ \sf 3x - 2y = 6 \end{cases}[/tex]
We'll substitute the expression for [tex]\sf y [/tex] from the first equation into the second equation:
[tex]\sf 3x - 2(2x + 3) = 6 [/tex]
Now, let's solve for [tex]\sf x [/tex]:
[tex]\sf 3x - 4x - 6 = 6 [/tex]
[tex]\sf -x - 6 = 6 [/tex]
[tex]\sf -x = 6 + 6 [/tex]
[tex]\sf -x = 12 [/tex]
[tex]\sf x = -12 [/tex]
Now that we have found the value of [tex]\sf x [/tex], we'll substitute it back into the first equation to find [tex]\sf y [/tex]:
[tex]\sf y = 2(-12) + 3 [/tex]
[tex]\sf y = -24 + 3 [/tex]
[tex]\sf y = -21 [/tex]
So, the solution to the system of equations is:
[tex]\sf x = -12 [/tex] and [tex]\sf y = -21 [/tex]
