Answered

Solve the following system of equations using the substitution method:

[tex]
\left\{
\begin{array}{ll}
7x - 6y &= -100 \\
x &= -2y
\end{array}
\right.
[/tex]

Answer: [tex]$\square$[/tex]



Answer :

Sure, let's solve the system of equations using the substitution method step-by-step:

We are given the system of equations:
[tex]\[ \left\{\begin{array}{ll} 7x - 6y & = -100 \\ x & = -2y \end{array}\right. \][/tex]

1. Substitute [tex]\(x = -2y\)[/tex] in the first equation:

The first equation is [tex]\(7x - 6y = -100\)[/tex].

Substitute [tex]\(x\)[/tex] from the second equation into the first equation:
[tex]\[ 7(-2y) - 6y = -100 \][/tex]

2. Simplify the first equation:

Simplify the expression:
[tex]\[ -14y - 6y = -100 \][/tex]
Combine like terms:
[tex]\[ -20y = -100 \][/tex]

3. Solve for [tex]\(y\)[/tex]:

Divide both sides of the equation by -20:
[tex]\[ y = \frac{-100}{-20} = 5 \][/tex]

4. Substitute [tex]\(y = 5\)[/tex] back into the second equation:

The second equation is [tex]\(x = -2y\)[/tex].
Substitute [tex]\(y = 5\)[/tex] into the equation:
[tex]\[ x = -2(5) = -10 \][/tex]

Therefore, the solution to the system of equations is:
[tex]\[ \boxed{(-10, 5)} \][/tex]
Where [tex]\(x = -10\)[/tex] and [tex]\(y = 5\)[/tex].