Solve the system of equations. {:[9x-4y=-7],[7x-12 y=39],[x=◻],[y=◻]:}

Identify Variable to Eliminate: Identify the variable to eliminate. We can choose to eliminate either 'x' or 'y'. In this case, we will eliminate 'y' by finding a common multiple for the coefficients of 'y' in both equations.Multiply Equations by Common Multiple: Multiply the first equation by 3 and the second equation by 1 to get the coefficients of 'y' to be the same (12). 3*(9x - 4y) = 3*(-7) gives 27x - 12y = -21. 1*(7x - 12y) = 1*(39) gives 7x - 12y = 39.Subtract Equations to Eliminate Variable: Subtract the second equation from the first to eliminate 'y'. (27x - 12y) - (7x - 12y) = -21 - 39 27x - 7x = -60 20x = -60Solve for x: Solve for 'x'. Divide both sides of the equation by 20 to find the value of 'x'. 20x / 20 = -60 / 20 x = -3Substitute x into Original Equation: Substitute x = -3 into the first original equation to solve for 'y'. 9(-3) - 4y = -7 -27 - 4y = -7Isolate Term with y: Add 27 to both sides of the equation to isolate the term with 'y'. -4y = -7 + 27 -4y = 20Solve for y: Solve for 'y'. Divide both sides of the equation by -4 to find the value of 'y'. -4y / -4 = 20 / -4 y = -5Write Solution as Coordinate Point: Write the solution as a coordinate point. The solution is (-3, -5).

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Solve the system of equations.

{:[9x-4y=-7],[7x-12 y=39],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 9 x-4 y=-7 \\ 7 x-12 y=39 \\ x=\square \\ y=\square \end{array}$

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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} 9 x-4 y=-7 \\ 7 x-12 y=39 \\ x=\square \\ y=\square \end{array}

Identify Variable to Eliminate: Identify the variable to eliminate. We can choose to eliminate either ' $x$ ' or ' $y$ '. In this case, we will eliminate ' $y$ ' by finding a common multiple for the coefficients of ' $y$ ' in both equations.
Multiply Equations by Common Multiple: Multiply the first equation by $3$ and the second equation by $1$ to get the coefficients of ' $y$ ' to be the same ( $12$ ). $\newline$ $3 \times (9x - 4y) = 3 \times (-7)$ gives $27x - 12y = -21$ . $\newline$ $1 \times (7x - 12y) = 1 \times (39)$ gives $7x - 12y = 39$ .
Subtract Equations to Eliminate Variable: Subtract the second equation from the first to eliminate 'y'. $\newline$ $(27x - 12y) - (7x - 12y) = -21 - 39$ $\newline$ $27x - 7x = -60$ $\newline$ $20x = -60$
Solve for x: Solve for 'x'. Divide both sides of the equation by $20$ to find the value of 'x'. $\newline$ $\frac{20x}{20} = \frac{-60}{20}$ $\newline$ $x = -3$
Substitute $x$ into Original Equation: Substitute $x = -3$ into the first original equation to solve for 'y'. $\newline$ $9(-3) - 4y = -7$ $\newline$ $-27 - 4y = -7$
Isolate Term with y: Add $27$ to both sides of the equation to isolate the term with 'y'. $\newline$ $-4y = -7 + 27$ $\newline$ $-4y = 20$
Solve for y: Solve for 'y'. Divide both sides of the equation by $-4$ to find the value of 'y'. $\frac{-4y}{-4} = \frac{20}{-4}$ $y = -5$
Write Solution as Coordinate Point: Write the solution as a coordinate point. The solution is $(-3, -5)$ .