If 5x-y=-7 and x-2y=2 are true equations, what would be the value of -4x-y ? Answer:

Identify Equations: Identify the system of equations. We have two equations: 1) 5x - y = -7 2) x - 2y = 2 We need to find the value of -4x - y.Solve for x: Solve one of the equations for one variable. Let's solve the second equation for x: x = 2y + 2Substitute x: Substitute the expression for x into the first equation. Replace x in the first equation with the expression from the second equation: 5(2y + 2) - y = -7Simplify for y: Simplify and solve for y. 10y + 10 - y = -7 9y + 10 = -7 9y = -17 y = -17 / 9Substitute y into x: Substitute the value of y back into the expression for x. x = 2(-17 / 9) + 2 x = -34 / 9 + 18 / 9 x = -16 / 9Calculate -4x - y: Calculate the value of -4x - y using the found values of x and y. -4x - y = -4(-16 / 9) - (-17 / 9) -4x - y = 64 / 9 + 17 / 9 -4x - y = 81 / 9 -4x - y = 9

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Grade 8

Describe the graph of a linear equation

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Q. If

5 \mathbf{x}-\mathbf{y}=-\mathbf{7}

and

\mathbf{x}-\mathbf{2 y}=\mathbf{2}

are true equations, what would be the value of

-4 x-y

\newline

Answer:

Identify Equations: Identify the system of equations. $\newline$ We have two equations: $\newline$ $1$ ) $5x - y = -7$ $\newline$ $2$ ) $x - 2y = 2$ $\newline$ We need to find the value of $-4x - y$ .
Solve for $x$ : Solve one of the equations for one variable. $\newline$ Let's solve the second equation for $x$ : $\newline$ $x = 2y + 2$
Substitute $x$ : Substitute the expression for $x$ into the first equation. $\newline$ Replace $x$ in the first equation with the expression from the second equation: $\newline$ $5(2y + 2) - y = -7$
Simplify for $y$ : Simplify and solve for $y$ . $10y + 10 - y = -7$ $9y + 10 = -7$ $9y = -17$ $y = -\frac{17}{9}$
Substitute $y$ into $x$ : Substitute the value of $y$ back into the expression for $x$ .
$x = 2(-17 / 9) + 2$
$x = -34 / 9 + 18 / 9$
$x = -16 / 9$
Calculate $-4x - y$ : Calculate the value of $-4x - y$ using the found values of $x$ and $y$ .
$-4x - y = -4(-16 / 9) - (-17 / 9)$
$-4x - y = 64 / 9 + 17 / 9$
$-4x - y = 81 / 9$
$-4x - y = 9$