4p-2t=6 8p+6t=12+2t Which of the following accurately describes all solutions to the system of equations shown? Choose 1 answer: (A) p=(3)/(2) and t=0 (B) p=3 and t=3 (c) There are infinite solutions to the system. (D) There are no solutions to the system.

Write down equations: Write down the system of equations. We have the following system of equations: 4p - 2t = 6 8p + 6t = 12 + 2tSimplify second equation: Simplify the second equation by subtracting 2t from both sides. 8p + 6t - 2t = 12 + 2t - 2t 8p + 4t = 12Compare coefficients: Compare the coefficients of the simplified system of equations. We now have: 4p - 2t = 6 8p + 4t = 12 Notice that the second equation is exactly twice the first equation.Determine solution type: Determine if the system has one solution, no solution, or infinitely many solutions. Since the second equation is a multiple of the first, the two equations are dependent, and the system has infinitely many solutions.

Home

Math Problems

Algebra 1

Solve rational equations

Full solution

4 p-2 t=6

\newline

8 p+6 t=12+2 t

\newline

Which of the following accurately describes all solutions to the system of equations shown?

\newline

Choose

1

answer:

\newline

(A)

p=\frac{3}{2}

and

t=0

\newline

(B)

p=3

and

t=3

\newline

\newline

(D) There are no solutions to the system.

Write down equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $4p - 2t = 6$ $\newline$ $8p + 6t = 12 + 2t$
Simplify second equation: Simplify the second equation by subtracting $2t$ from both sides. $\newline$ $8p + 6t - 2t = 12 + 2t - 2t$ $\newline$ $8p + 4t = 12$
Compare coefficients: Compare the coefficients of the simplified system of equations. $\newline$ We now have: $\newline$ $4p - 2t = 6$ $\newline$ $8p + 4t = 12$ $\newline$ Notice that the second equation is exactly twice the first equation.
Determine solution type: Determine if the system has one solution, no solution, or infinitely many solutions. $\newline$ Since the second equation is a multiple of the first, the two equations are dependent, and the system has infinitely many solutions.