How many solutions does the system have? {[y=-2x-4],[y=3x+3]:} Choose 1 answer: (A) Exactly one solution (B) No solutions C) Infinitely many solutions

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How many solutions does the system have?  {[y=-2x-4],[y=3x+3]:} Choose 1 answer: (A) Exactly one solution (B) No solutions C) Infinitely many solutions

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Write Equations: Write down the system of equations. We have the following system of equations: y = -2x - 4 y = 3x + 3Set Equal: Since both equations are equal to y, set them equal to each other to find the point of intersection. -2x - 4 = 3x + 3Solve for x: Solve for x by adding 2x to both sides and adding 4 to both sides. -2x + 2x - 4 + 4 = 3x + 2x + 3 + 4 0x = 5x + 7Simplify Equation: Simplify the equation. 0 = 5x + 7Isolate x: Subtract 7 from both sides to isolate the x-term. -7 = 5xDivide by 5: Divide both sides by 5 to solve for x. x = -7/5Substitute x: Substitute x back into one of the original equations to solve for y. Using y = -2x - 4: y = -2(-7/5) - 4Multiply and Subtract: Multiply -2 by -7/5 and subtract 4. y = 14/5 - 4Combine Fractions: Convert 4 to a fraction with a denominator of 5 to combine with 14/5. y = 14/5 - 20/5Final Solution: Subtract the fractions. y = (14 - 20)/5 y = -6/5We have found a single solution for the system of equations: (x, y) = (-7/5, -6/5). This means the system has exactly one solution where the two lines intersect at one point.

How many solutions does the system have? $\begin{cases} y = -2x - 4 \newline\ y = 3x + 3 \end{cases}$ Choose $1$ answer: $\newline$ $(A)$ Exactly one solution $\newline$ $(B)$ No solutions $\newline$ $(C)$ Infinitely many solutions

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How many solutions does the system have?{y=−2x−4 y=3x+3\begin{cases} y = -2x - 4 \newline\ y = 3x + 3 \end{cases}{y=−2x−4 y=3x+3​Choose 111 answer:\newline(A) (A) (A) Exactly one solution\newline(B) (B) (B) No solutions\newline(C) (C)(C) Infinitely many solutions

How many solutions does the system have? $\begin{cases} y = -2x - 4 \newline\ y = 3x + 3 \end{cases}$ Choose $1$ answer: $\newline$ $(A)$ Exactly one solution $\newline$ $(B)$ No solutions $\newline$ $(C)$ Infinitely many solutions