Question

Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. If thesystem has one solution, find th e solution3x + 3y = -212x + y = - 15

Answer 1

Isolating the variable y in the second equation, we have:

$\begin{gathered} 2x+y=-15 \\ y=-15-2x \end{gathered}$

Now, using this value of y in the first equation, we have:

$\begin{gathered} 3x+3y=-21 \\ 3x+3(-15-2x)=-21 \\ 3x-45-6x=-21 \\ -3x=-21+45 \\ -3x=24 \\ x=\frac{24}{-3}=-8 \\ \\ y=-15-2\cdot(-8)=-15+16=1 \end{gathered}$

The solution of the system is x = -8 and y = 1.