Solve the system of equations. {:[-3y+4x=13],[-5y-6x=-67],[x=◻],[y=◻]:}

Identify variable to eliminate: Identify the variable to eliminate. In this case, we can choose to eliminate 'y' by multiplying the first equation by 5 and the second equation by 3 to make the coefficients of 'y' opposites.Multiply equations by coefficients: Multiply the first equation by 5 and the second equation by 3. First equation: 5(-3y + 4x) = 5(13) gives -15y + 20x = 65. Second equation: 3(-5y - 6x) = 3(-67) gives -15y - 18x = -201.Add equations to eliminate variable: Add the equations to eliminate 'y'. (-15y + 20x) + (-15y - 18x) = 65 - 201 -15y + 20x - 15y - 18x = -136 This simplifies to 2x = -136.Solve for x: Solve for 'x'. Dividing both sides of the equation by 2 gives us x = -68.Substitute x into first equation: Substitute x = -68 into the first equation to solve for 'y'. Substitute x = -68 in -3y + 4x = 13. We get -3y + 4(-68) = 13. This simplifies to -3y - 272 = 13.Solve for y: Solve for 'y'. Add 272 to both sides of the equation to get -3y = 285. Then divide by -3 to get y = -95.Write solution as coordinate point: Write the solution as a coordinate point. The solution is (-68, -95).

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Solve the system of equations.

{:[-3y+4x=13],[-5y-6x=-67],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -3 y+4 x=13 \\ -5 y-6 x=-67 \\ x=\square \\ y=\square \end{array}$

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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} -3 y+4 x=13 \\ -5 y-6 x=-67 \\ x=\square \\ y=\square \end{array}

Identify variable to eliminate: Identify the variable to eliminate. In this case, we can choose to eliminate ' $y$ ' by multiplying the first equation by $5$ and the second equation by $3$ to make the coefficients of ' $y$ ' opposites.
Multiply equations by coefficients: Multiply the first equation by $5$ and the second equation by $3$ . $\newline$ First equation: $5(-3y + 4x) = 5(13)$ gives $-15y + 20x = 65$ . $\newline$ Second equation: $3(-5y - 6x) = 3(-67)$ gives $-15y - 18x = -201$ .
Add equations to eliminate variable: Add the equations to eliminate 'y'. $\newline$ $(-15y + 20x) + (-15y - 18x) = 65 - 201$ $\newline$ $-15y + 20x - 15y - 18x = -136$ $\newline$ This simplifies to $2x = -136$ .
Solve for x: Solve for 'x'. Dividing both sides of the equation by $2$ gives us $x = -68$ .
Substitute $x$ into first equation: Substitute $x = -68$ into the first equation to solve for 'y'. $\newline$ Substitute $x = -68$ in $-3y + 4x = 13$ . We get $-3y + 4(-68) = 13$ . $\newline$ This simplifies to $-3y - 272 = 13$ .
Solve for y: Solve for 'y'. Add $272$ to both sides of the equation to get $-3y = 285$ . Then divide by $-3$ to get $y = -95$ .
Write solution as coordinate point: Write the solution as a coordinate point. The solution is $(-68, -95)$ .