Solve the system of equations. {:[13 x+2y=1],[5x-2y=-19],[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 'y' because the coefficients of 'y' are opposite in both equations.Add equations to eliminate 'y': Add the equations to eliminate 'y'. (13x + 2y) + (5x - 2y) = 1 + (-19) 13x + 2y + 5x - 2y = 1 - 19 18x = -18Solve for 'x': Solve for 'x'. Divide both sides of the equation by 18 to find the value of 'x'. 18x / 18 = -18 / 18 x = -1Substitute x = -1 to solve for 'y': Substitute x = -1 into one of the original equations to solve for 'y'. We can use the first equation 13x + 2y = 1. 13(-1) + 2y = 1 -13 + 2y = 1Solve for 'y': Solve for 'y'. Add 13 to both sides of the equation to isolate the term with 'y'. 2y = 1 + 13 2y = 14Divide both sides of the equation by 2 to find the value of 'y'. 2y / 2 = 14 / 2 y = 7

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Solve the system of equations.

{:[13 x+2y=1],[5x-2y=-19],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 13 x+2 y=1 \\ 5 x-2 y=-19 \\ x=\square \\ y=\square \end{array}$

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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} 13 x+2 y=1 \\ 5 x-2 y=-19 \\ 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 ' $y$ ' because the coefficients of ' $y$ ' are opposite in both equations.
Add equations to eliminate 'y': Add the equations to eliminate 'y'. $(13x + 2y) + (5x - 2y) = 1 + (-19)$ $\newline$ $13x + 2y + 5x - 2y = 1 - 19$ $\newline$ $18x = -18$
Solve for 'x': Solve for 'x'. Divide both sides of the equation by $18$ to find the value of 'x'. $\newline$ $\frac{18x}{18} = \frac{-18}{18}$ $\newline$ $x = -1$
Substitute $x = -1$ to solve for 'y': Substitute $x = -1$ into one of the original equations to solve for 'y'. We can use the first equation $13x + 2y = 1$ .
$13(-1) + 2y = 1$
$-13 + 2y = 1$
Solve for 'y': Solve for 'y'. Add $13$ to both sides of the equation to isolate the term with 'y'. $\newline$ $2y = 1 + 13$ $\newline$ $2y = 14$
Solve for 'y': Solve for 'y'. Add $13$ to both sides of the equation to isolate the term with 'y'. $\newline$ $2y = 1 + 13$ $\newline$ $2y = 14$ Divide both sides of the equation by $2$ to find the value of 'y'. $\newline$ $\frac{2y}{2} = \frac{14}{2}$ $\newline$ $y = 7$