Solve the system of equations. {:[4x-9y-2=0],[12 x-5y+38=0],[x=◻],[y=◻]:}

Multiply equation by 3: Multiply the first equation by 3 to align the coefficient of x in both equations. Calculation: 3 * (4x - 9y - 2) = 3 * 0 This gives us 12x - 27y - 6 = 0.Subtract equations to eliminate x: Subtract the second equation from the modified first equation to eliminate x. Calculation: (12x - 27y - 6) - (12x - 5y + 38) = 0 - 0 This simplifies to -27y + 5y - 6 - 38 = 0, which further simplifies to -22y - 44 = 0.Solve for y: Solve for y. Calculation: -22y - 44 = 0 Add 44 to both sides: -22y = 44 Divide by -22: y = 44 / -22 This gives us y = -2.Substitute y into first equation: Substitute y = -2 into the first original equation to solve for x. Calculation: 4x - 9(-2) - 2 = 0 This simplifies to 4x + 18 - 2 = 0, which further simplifies to 4x + 16 = 0.Solve for x: Solve for x. Calculation: 4x + 16 = 0 Subtract 16 from both sides: 4x = -16 Divide by 4: x = -16 / 4 This gives us x = -4.Check the solution: Check the solution by substituting x = -4 and y = -2 into the second original equation. Calculation: 12(-4) - 5(-2) + 38 = 0 This simplifies to -48 + 10 + 38 = 0, which further simplifies to 0 = 0.

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Solve the system of equations.

{:[4x-9y-2=0],[12 x-5y+38=0],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 4 x-9 y-2=0 \\ 12 x-5 y+38=0 \\ x=\square \\ y=\square \end{array}$

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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} 4 x-9 y-2=0 \\ 12 x-5 y+38=0 \\ x=\square \\ y=\square \end{array}

Multiply equation by $3$ : Multiply the first equation by $3$ to align the coefficient of $x$ in both equations. $\newline$ Calculation: $3 \times (4x - 9y - 2) = 3 \times 0$ $\newline$ This gives us $12x - 27y - 6 = 0$ .
Subtract equations to eliminate x: Subtract the second equation from the modified first equation to eliminate x. $\newline$ Calculation: $(12x - 27y - 6) - (12x - 5y + 38) = 0 - 0$ $\newline$ This simplifies to $-27y + 5y - 6 - 38 = 0$ , which further simplifies to $-22y - 44 = 0$ .
Solve for y: Solve for y. $\newline$ Calculation: $-22y - 44 = 0$ $\newline$ Add $44$ to both sides: $-22y = 44$ $\newline$ Divide by $-22$ : $y = \frac{44}{-22}$ $\newline$ This gives us $y = -2$ .
Substitute $y$ into first equation: Substitute $y = -2$ into the first original equation to solve for $x$ . $\newline$ Calculation: $4x - 9(-2) - 2 = 0$ $\newline$ This simplifies to $4x + 18 - 2 = 0$ , which further simplifies to $4x + 16 = 0$ .
Solve for x: Solve for x. $\newline$ Calculation: $4x + 16 = 0$ $\newline$ Subtract $16$ from both sides: $4x = -16$ $\newline$ Divide by $4$ : $x = \frac{-16}{4}$ $\newline$ This gives us $x = -4$ .
Check the solution: Check the solution by substituting $x = -4$ and $y = -2$ into the second original equation. $\newline$ Calculation: $12(-4) - 5(-2) + 38 = 0$ $\newline$ This simplifies to $-48 + 10 + 38 = 0$ , which further simplifies to $0 = 0$ .