Solve the system of equations. {:[-6y+11 x=-36],[-4y+7x=-24],[x=◻],[y=◻]:}

Write Equations: Write down the system of equations. We have the following system of equations: -6y + 11x = -36 -4y + 7x = -24 We need to find the values of x and y that satisfy both equations.Solve for x: Solve one of the equations for one variable. Let's solve the second equation for x: -4y + 7x = -24 7x = 4y - 24 x = (4y - 24) / 7 Now we have x expressed in terms of y.Substitute x: Substitute the expression for x into the first equation. Substitute x = (4y - 24) / 7 into the first equation: -6y + 11((4y - 24) / 7) = -36 Now we need to solve for y.Eliminate Fraction: Multiply both sides of the equation by 7 to eliminate the fraction. 7(-6y) + 11(4y - 24) = -36 * 7 -42y + 44y - 264 = -252 Now we combine like terms.Combine Terms: Combine like terms and solve for y. 2y - 264 = -252 2y = -252 + 264 2y = 12 y = 12 / 2 y = 6 We have found the value of y.Find y: Substitute the value of y back into the expression for x. x = (4y - 24) / 7 x = (4(6) - 24) / 7 x = (24 - 24) / 7 x = 0 / 7 x = 0 We have found the value of x.

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Solve the system of equations.

{:[-6y+11 x=-36],[-4y+7x=-24],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -6 y+11 x=-36 \\ -4 y+7 x=-24 \\ x=\square \\ y=\square \end{array}$

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Algebra 2

Solve a system of equations using elimination

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Q. Solve the system of equations.

\newline

\begin{array}{l} -6 y+11 x=-36 \\ -4 y+7 x=-24 \\ x=\square \\ y=\square \end{array}

Write Equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $-6y + 11x = -36$ $\newline$ $-4y + 7x = -24$ $\newline$ We need to find the values of $x$ and $y$ that satisfy both equations.
Solve for x: Solve one of the equations for one variable. $\newline$ Let's solve the second equation for x: $\newline$ $-4y + 7x = -24$ $\newline$ $7x = 4y - 24$ $\newline$ $x = \frac{4y - 24}{7}$ $\newline$ Now we have $x$ expressed in terms of $y$ .
Substitute $x$ : Substitute the expression for $x$ into the first equation. $\newline$ Substitute $x = \frac{4y - 24}{7}$ into the first equation: $\newline$ -6y + 11\left(\frac{4y - 24}{7}\right) = -36$\newlineNow we need to solve for \$y$.
Eliminate Fraction: Multiply both sides of the equation by $7$ to eliminate the fraction.$\newline$$7(-6y) + 11(4y - 24) = -36 \times 7$$\newline$$-42y + 44y - 264 = -252$$\newline$Now we combine like terms.
Combine Terms: Combine like terms and solve for $y$. $\newline$\[2y - 264 = -252\]$\newline$\[2y = -252 + 264\]$\newline$\[2y = 12\]$\newline$\[y = \frac{12}{2}\]$\newline$\[y = 6\]$\newline$We have found the value of $y$.
Find $y$: Substitute the value of $y$ back into the expression for $x$.
$x = \frac{4y - 24}{7}$
$x = \frac{4(6) - 24}{7}$
$x = \frac{24 - 24}{7}$
$x = \frac{0}{7}$
$x = 0$
We have found the value of $x$.