How many solutions does the system have? {[6x-y=-1],[6x+y=-1]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (c) Infinitely many solutions

Write equations: Write down the system of equations. We have the following system of equations: 6x - y = -1 6x + y = -1Compare coefficients: Compare the two equations. Both equations have the same coefficient for x, which is 6. This means they have the same slope.Differences in equations: Look for differences in the equations. The equations differ only by the sign of y. The first equation has -y, and the second has +y.Eliminate y: Add the two equations together to eliminate y. (6x - y) + (6x + y) = -1 + (-1) 12x = -2Solve for x: Solve for x. Divide both sides by 12 to isolate x: x = -2 / 12 x = -1/6Substitute x into equation: Substitute x back into one of the original equations to find y. Using the first equation: 6(-1/6) - y = -1 -1 - y = -1 y = 0Check solution in second equation: Check the solution in the second equation. 6(-1/6) + y = -1 -1 + y = -1 y = 0Conclude number of solutions: Conclude the number of solutions. Since we found a single value for x and y that satisfies both equations, the system has exactly one solution.

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How many solutions does the system have?

{[6x-y=-1],[6x+y=-1]:}
Choose 1 answer:
(A) Exactly one solution
(B) No solutions
(c) Infinitely many solutions

How many solutions does the system have? $\newline$ $\left\{\begin{array}{l} 6 x-y=-1 \\ 6 x+y=-1 \end{array}\right.$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions

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Algebra 2

Find the number of solutions to a system of equations

Full solution

Q. How many solutions does the system have?

\newline

\left\{\begin{array}{l} 6 x-y=-1 \\ 6 x+y=-1 \end{array}\right.

\newline

Choose

1

answer:

\newline

(A) Exactly one solution

\newline

(B) No solutions

\newline

Write equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $6x - y = -1$ $\newline$ $6x + y = -1$
Compare coefficients: Compare the two equations. $\newline$ Both equations have the same coefficient for $x$ , which is $6$ . This means they have the same slope.
Differences in equations: Look for differences in the equations. $\newline$ The equations differ only by the sign of $y$ . The first equation has $-y$ , and the second has $+y$ .
Eliminate y: Add the two equations together to eliminate y. $\newline$ $(6x - y) + (6x + y) = -1 + (-1)$ $\newline$ $12x = -2$
Solve for x: Solve for x. $\newline$ Divide both sides by $12$ to isolate x: $\newline$ $x = \frac{-2}{12}$ $\newline$ $x = \frac{-1}{6}$
Substitute $x$ into equation: Substitute $x$ back into one of the original equations to find $y$ . $\newline$ Using the first equation: $\newline$ $6(-\frac{1}{6}) - y = -1$ $\newline$ $-1 - y = -1$ $\newline$ $y = 0$
Check solution in second equation: Check the solution in the second equation. $\newline$ $6(-\frac{1}{6}) + y = -1$ $\newline$ $-1 + y = -1$ $\newline$ $y = 0$
Conclude number of solutions: Conclude the number of solutions. $\newline$ Since we found a single value for $x$ and $y$ that satisfies both equations, the system has exactly one solution.