Solve the system of equations. {:[3x-4y=8],[18 x-5y=10],[x=◻],[y=◻]:}

Step 1: Eliminate variable 'x': Identify the variable to eliminate. We can eliminate 'x' by multiplying the first equation by 6 to match the coefficient of 'x' in the second equation. Calculation: 6 * (3x - 4y) = 6 * 8 This gives us 18x - 24y = 48.Step 2: Subtract equations to eliminate 'x': Subtract the modified first equation from the second equation to eliminate 'x'. Calculation: (18x - 5y) - (18x - 24y) = 10 - 48 This simplifies to 19y = -38.Step 3: Solve for 'y': Solve for 'y'. Calculation: Divide both sides of the equation by 19 to get y = -38 / 19, which simplifies to y = -2.Step 4: Substitute 'y' into first equation: Substitute y = -2 into the first original equation to solve for 'x'. Calculation: 3x - 4(-2) = 8 This simplifies to 3x + 8 = 8.Step 5: Solve for 'x': Solve for 'x'. Calculation: Subtract 8 from both sides to get 3x = 0, then divide by 3 to get x = 0.Step 6: Write the solution as a coordinate point: Write the solution as a coordinate point. The solution is (0, -2).

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Solve the system of equations.

{:[3x-4y=8],[18 x-5y=10],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 3 x-4 y=8 \\ 18 x-5 y=10 \\ x=\square \\ y=\square \end{array}$

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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 x-4 y=8 \\ 18 x-5 y=10 \\ x=\square \\ y=\square \end{array}

Step $1$ : Eliminate variable 'x': Identify the variable to eliminate. We can eliminate 'x' by multiplying the first equation by $6$ to match the coefficient of 'x' in the second equation. $\newline$ Calculation: $6 \times (3x - 4y) = 6 \times 8$ $\newline$ This gives us $18x - 24y = 48$ .
Step $2$ : Subtract equations to eliminate 'x': Subtract the modified first equation from the second equation to eliminate 'x'. $\newline$ Calculation: $(18x - 5y) - (18x - 24y) = 10 - 48$ $\newline$ This simplifies to $19y = -38$ .
Step $3$ : Solve for 'y': Solve for 'y'. $\newline$ Calculation: Divide both sides of the equation by $19$ to get $y = \frac{-38}{19}$ , which simplifies to $y = -2$ .
Step $4$ : Substitute 'y' into first equation: Substitute $y = -2$ into the first original equation to solve for 'x'. $\newline$ Calculation: $3x - 4(-2) = 8$ $\newline$ This simplifies to $3x + 8 = 8$ .
Step $5$ : Solve for 'x': Solve for 'x'. $\newline$ Calculation: Subtract $8$ from both sides to get $3x = 0$ , then divide by $3$ to get $x = 0$ .
Step $6$ : Write the solution as a coordinate point: Write the solution as a coordinate point. $\newline$ The solution is $(0, -2)$ .