Solve the system of equations. {:[2y+7x=-5],[5y-7x=12],[x=◻],[y=◻]:}

Identify variable to eliminate: Identify the variable to eliminate. In this case, we can eliminate 'x' as the coefficients are the opposite in both equations.Identify operation to eliminate variable: Identify the operation to eliminate the variable. Here, we add the equations as the coefficients are opposite.Add equations to eliminate 'x': Add the equations to eliminate 'x'. (2y + 7x) + (5y - 7x) = -5 + 12 2y + 7x + 5y - 7x = 7 7y = 7 This gives us 7y = 7.Solve for 'y': Solve for 'y'. Dividing both sides of the equation by 7 gives us y = 1.Substitute y = 1 to solve for 'x': Substitute y = 1 into the first equation to solve for 'x'. Substitute y = 1 in 2y + 7x = -5. We get 2(1) + 7x = -5. Simplify to get 2 + 7x = -5. Subtract 2 from both sides, we get 7x = -7. Divide by 7, we get x = -1. This gives us x = -1.Write solution as a coordinate point: Write the solution as a coordinate point. The solution is (-1, 1).

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Solve the system of equations.

{:[2y+7x=-5],[5y-7x=12],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 2 y+7 x=-5 \\ 5 y-7 x=12 \\ x=\square \\ y=\square \end{array}$

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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+7 x=-5 \\ 5 y-7 x=12 \\ x=\square \\ y=\square \end{array}

Identify variable to eliminate: Identify the variable to eliminate. In this case, we can eliminate ' $x$ ' as the coefficients are the opposite in both equations.
Identify operation to eliminate variable: Identify the operation to eliminate the variable. Here, we add the equations as the coefficients are opposite.
Add equations to eliminate 'x': Add the equations to eliminate 'x'. $(2y + 7x) + (5y - 7x) = -5 + 12$ $2y + 7x + 5y - 7x = 7$ $7y = 7$ This gives us $7y = 7$ .
Solve for 'y': Solve for 'y'. Dividing both sides of the equation by $7$ gives us $y = 1$ .
Substitute $y = 1$ to solve for ' $x$ ': Substitute $y = 1$ into the first equation to solve for ' $x$ '. Substitute $y = 1$ in $2y + 7x = -5$ . We get $2(1) + 7x = -5$ . Simplify to get $2 + 7x = -5$ . Subtract $2$ from both sides, we get $7x = -7$ . Divide by $x$ $0$ , we get $x$ $1$ . This gives us $x$ $1$ .
Write solution as a coordinate point: Write the solution as a coordinate point. The solution is $(-1, 1)$ .