How many solutions does the given system of equations have? y-7=-6(x+1) 4y+24 x+28=0

Write Equations: Write down the given system of equations. The system of equations is: y - 7 = -6(x + 1) 4y + 24x + 28 = 0Simplify First Equation: Simplify the first equation to express y in terms of x. y - 7 = -6(x + 1) y = -6x - 6 + 7 y = -6x + 1Substitute into Second Equation: Substitute the expression for y from the first equation into the second equation. 4(-6x + 1) + 24x + 28 = 0 -24x + 4 + 24x + 28 = 0Combine Like Terms: Simplify the equation by combining like terms. -24x + 24x + 4 + 28 = 0 0x + 32 = 0Solve for x: Solve the simplified equation for x. Since there is no x term left (0x = 0), we only have a constant left on the left side of the equation. 32 = 0 This is a contradiction because 32 cannot equal 0.Conclude No Solutions: Conclude the number of solutions based on the contradiction. Since we arrived at a contradiction, it means that there are no values of x and y that can satisfy both equations simultaneously. Therefore, the system of equations has no solutions.

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Q. How many solutions does the given system of equations have?

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y-7=-6(x+1)

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4y+24x+28=0

Write Equations: Write down the given system of equations. $\newline$ The system of equations is: $\newline$ $y - 7 = -6(x + 1)$ $\newline$ $4y + 24x + 28 = 0$
Simplify First Equation: Simplify the first equation to express $y$ in terms of $x$ . $y - 7 = -6(x + 1)$ $y = -6x - 6 + 7$ $y = -6x + 1$
Substitute into Second Equation: Substitute the expression for $y$ from the first equation into the second equation. $4(-6x + 1) + 24x + 28 = 0$ $-24x + 4 + 24x + 28 = 0$
Combine Like Terms: Simplify the equation by combining like terms. $\newline$ $-24x + 24x + 4 + 28 = 0$ $\newline$ $0x + 32 = 0$
Solve for x: Solve the simplified equation for x. $\newline$ Since there is no x term left ( $0x = 0$ ), we only have a constant left on the left side of the equation. $\newline$ $32 = 0$ $\newline$ This is a contradiction because $32$ cannot equal $0$ .
Conclude No Solutions: Conclude the number of solutions based on the contradiction. $\newline$ Since we arrived at a contradiction, it means that there are no values of $x$ and $y$ that can satisfy both equations simultaneously. Therefore, the system of equations has no solutions.