Solve the system of equations. {:[2y-3x=-27],[5y+3x=6],[x=◻],[y=◻]:}

Identify operation to eliminate variable: Identify the operation to eliminate one of the variables. In this case, we can add the two equations directly to eliminate 'x'.Add equations to eliminate 'x': Add the equations (2y - 3x) + (5y + 3x) = -27 + 6. This simplifies to 2y + 5y = -27 + 6, which gives us 7y = -21.Solve for 'y': Solve for 'y'. Dividing both sides of the equation by 7 gives us y = -21 / 7, which simplifies to y = -3.Substitute y into equation: Substitute y = -3 into one of the original equations to solve for 'x'. We can use the first equation 2y - 3x = -27. Substituting y gives us 2(-3) - 3x = -27.Simplify equation and solve for 'x': Simplify the equation and solve for 'x'. This gives us -6 - 3x = -27. Adding 6 to both sides gives us -3x = -27 + 6, which simplifies to -3x = -21.Divide both sides to solve for 'x': Divide both sides by -3 to solve for 'x'. This gives us x = -21 / -3, which simplifies to x = 7.Write solution as coordinate point: Write the solution as a coordinate point. The solution is (7, -3).

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Solve the system of equations.

{:[2y-3x=-27],[5y+3x=6],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 2 y-3 x=-27 \\ 5 y+3 x=6 \\ x=\square \\ y=\square \end{array}$

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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} 2 y-3 x=-27 \\ 5 y+3 x=6 \\ x=\square \\ y=\square \end{array}

Identify operation to eliminate variable: Identify the operation to eliminate one of the variables. In this case, we can add the two equations directly to eliminate ' $x$ '.
Add equations to eliminate 'x': Add the equations $(2y - 3x) + (5y + 3x) = -27 + 6$ . $\newline$ This simplifies to $2y + 5y = -27 + 6$ , which gives us $7y = -21$ .
Solve for 'y': Solve for 'y'. Dividing both sides of the equation by $7$ gives us $y = -\frac{21}{7}$ , which simplifies to $y = -3$ .
Substitute $y$ into equation: Substitute $y = -3$ into one of the original equations to solve for ' $x$ '. We can use the first equation $2y - 3x = -27$ . Substituting $y$ gives us $2(-3) - 3x = -27$ .
Simplify equation and solve for 'x': Simplify the equation and solve for 'x'. This gives us $-6 - 3x = -27$ . Adding $6$ to both sides gives us $-3x = -27 + 6$ , which simplifies to $-3x = -21$ .
Divide both sides to solve for 'x': Divide both sides by $-3$ to solve for 'x'. This gives us $x = \frac{-21}{-3}$ , which simplifies to $x = 7$ .
Write solution as coordinate point: Write the solution as a coordinate point. The solution is $(7, -3)$ .