Solve the system of equations. {:[5x-4y=-10],[-4x+5y=8],[x=◻],[y=◻]:}

Identify variable to eliminate: Identify the variable to eliminate. In this case, we can choose to eliminate either 'x' or 'y' since neither coefficient is a direct multiple of the other. Let's eliminate 'x' by multiplying the first equation by 4 and the second equation by 5 to get the coefficients of 'x' to be opposites.Multiply equations by coefficients: Multiply the first equation by 4 and the second equation by 5. First equation: (5x - 4y) * 4 = -10 * 4, which gives us 20x - 16y = -40. Second equation: (-4x + 5y) * 5 = 8 * 5, which gives us -20x + 25y = 40.Add equations to eliminate 'x': Add the new equations to eliminate 'x'. (20x - 16y) + (-20x + 25y) = -40 + 40 20x - 20x - 16y + 25y = 0 0x + 9y = 0 This simplifies to 9y = 0.Solve for 'y': Solve for 'y'. Dividing both sides of the equation by 9 gives us y = 0.Substitute 'y' into first equation: Substitute y = 0 into the first original equation to solve for 'x'. Substitute y = 0 in 5x - 4y = -10. We get 5x - 4(0) = -10. This simplifies to 5x = -10.Solve for 'x': Solve for 'x'. Dividing both sides of the equation by 5 gives us x = -10 / 5, which simplifies to x = -2.Write solution as coordinate point: Write the solution as a coordinate point. The solution is (-2, 0).

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Solve the system of equations.

{:[5x-4y=-10],[-4x+5y=8],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 5 x-4 y=-10 \\ -4 x+5 y=8 \\ x=\square \\ y=\square \end{array}$

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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} 5 x-4 y=-10 \\ -4 x+5 y=8 \\ x=\square \\ y=\square \end{array}

Identify variable to eliminate: Identify the variable to eliminate. In this case, we can choose to eliminate either ' $x$ ' or ' $y$ ' since neither coefficient is a direct multiple of the other. Let's eliminate ' $x$ ' by multiplying the first equation by $4$ and the second equation by $5$ to get the coefficients of ' $x$ ' to be opposites.
Multiply equations by coefficients: Multiply the first equation by $4$ and the second equation by $5$ .
First equation: $(5x - 4y) \times 4 = -10 \times 4$ , which gives us $20x - 16y = -40$ .
Second equation: $(-4x + 5y) \times 5 = 8 \times 5$ , which gives us $-20x + 25y = 40$ .
Add equations to eliminate 'x': Add the new equations to eliminate 'x'. $\newline$ $(20x - 16y) + (-20x + 25y) = -40 + 40$ $\newline$ $20x - 20x - 16y + 25y = 0$ $\newline$ $0x + 9y = 0$ $\newline$ This simplifies to $9y = 0$ .
Solve for 'y': Solve for 'y'. Dividing both sides of the equation by $9$ gives us $y = 0$ .
Substitute 'y' into first equation: Substitute $y = 0$ into the first original equation to solve for 'x'. $\newline$ Substitute $y = 0$ in $5x - 4y = -10$ . We get $5x - 4(0) = -10$ . This simplifies to $5x = -10$ .
Solve for 'x': Solve for 'x'. Dividing both sides of the equation by $5$ gives us $x = -10 / 5$ , which simplifies to $x = -2$ .
Write solution as coordinate point: Write the solution as a coordinate point. The solution is $(-2, 0)$ .