Solve the system of equations. {:[-7x-10 y=45],[-3x-5y=25],[x=◻],[y=◻]:}

Identify operation for elimination: Identify the operation to eliminate one of the variables. In this case, we notice that the coefficients of y in both equations are multiples of each other. We can multiply the second equation by 2 to match the coefficients of y in the first equation.Multiply second equation by 2: Multiply the second equation by 2 to prepare for elimination. -3x - 5y = 25 becomes -6x - 10y = 50.Add equations to eliminate y: Add the first equation to the new version of the second equation to eliminate y. (-7x - 10y) + (-6x - 10y) = 45 + 50 -7x - 6x - 10y - 10y = 95 -13x - 20y = 95Correct previous step: Realize that there has been a mistake in the previous step. The y terms should have been eliminated after adding the equations. We need to correct this error.

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Solve the system of equations.

{:[-7x-10 y=45],[-3x-5y=25],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -7 x-10 y=45 \\ -3 x-5 y=25 \\ x=\square \\ y=\square \end{array}$

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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} -7 x-10 y=45 \\ -3 x-5 y=25 \\ x=\square \\ y=\square \end{array}

Identify operation for elimination: Identify the operation to eliminate one of the variables. In this case, we notice that the coefficients of $y$ in both equations are multiples of each other. We can multiply the second equation by $2$ to match the coefficients of $y$ in the first equation.
Multiply second equation by $2$ : Multiply the second equation by $2$ to prepare for elimination. $\newline$ $-3x - 5y = 25$ becomes $-6x - 10y = 50$ .
Add equations to eliminate y: Add the first equation to the new version of the second equation to eliminate y. $\newline$ $(-7x - 10y) + (-6x - 10y) = 45 + 50$ $\newline$ $-7x - 6x - 10y - 10y = 95$ $\newline$ $-13x - 20y = 95$
Correct previous step: Realize that there has been a mistake in the previous step. The $y$ terms should have been eliminated after adding the equations. We need to correct this error.