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Solve the system with the addition method:

{[-12 x-8y,=-6],[6x+4y,=3]:}
Answer:
◻ ,
◻

Solve the system with the addition method: $\newline$ $\left\{\begin{array}{ll} -12 x-8 y & =-6 \\ 6 x+4 y & =3 \end{array}\right.$ $\newline$ Answer: $\square$ , $\square$

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Write an equation word problem

Full solution

Q. Solve the system with the addition method:

\newline

\left\{\begin{array}{ll} -12 x-8 y & =-6 \\ 6 x+4 y & =3 \end{array}\right.

\newline

Answer:

\square

,

\square

Write Equations: Step $1$ : Write down the system of equations. $\newline$ $\begin{cases} -12x - 8y = -6 \\ 6x + 4y = 3 \end{cases}$
Multiply Second Equation: Step $2$ : Multiply the second equation by $2$ to align the coefficients of $x$ for elimination. $\newline$ $\begin{cases} -12x - 8y = -6 \\ 12x + 8y = 6 \end{cases}$
Add Equations: Step $3$ : Add the two equations together to eliminate $y$ . $\newline$ $-12x - 8y + 12x + 8y = -6 + 6$ $\newline$ $0 = 0$
Infinite Solutions: Step $4$ : Since the variables cancel out and we are left with a true statement $0=0$ , the system has infinitely many solutions.

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