Solve the following system of equations. {:[8x-5y=25],[-2x+7y=11]:} {:[x=],[y=]:}

Set up equations: Step 1: Set up the equations for elimination. Given equations: 1) 8x - 5y = 25 2) -2x + 7y = 11 We aim to eliminate one variable by making the coefficients of x or y equal in both equations. Multiply second equation: Step 2: Multiply the second equation by 4 to align the coefficients of x. Original second equation: -2x + 7y = 11 Multiply by 4: -8x + 28y = 44 Now, the equations are: 1) 8x - 5y = 25 2) -8x + 28y = 44 Add equations to eliminate x: Step 3: Add the two equations to eliminate x. (8x - 5y) + (-8x + 28y) = 25 + 44 0x + 23y = 69 Simplify: y = 69 / 23 y = 3 Substitute to find x: Step 4: Substitute y = 3 back into one of the original equations to find x. Using the first equation: 8x - 5y = 25 Substitute y: 8x - 5(3) = 25 8x - 15 = 25 8x = 25 + 15 8x = 40 x = 40 / 8 x = 5

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Solve the following system of equations.

{:[8x-5y=25],[-2x+7y=11]:}

{:[x=],[y=]:}

Solve the following system of equations. $\newline$ $8x-5y=25$ $\newline$ $-2x+7y=11$ $\newline$ $x =$ $\square$ $\newline$ $y =$ $\square$

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Q. Solve the following system of equations.

\newline

8x-5y=25

\newline

-2x+7y=11

\newline

x =

\square

\newline

y =

\square

Set up equations: Step $1$ : Set up the equations for elimination. $\newline$ Given equations: $\newline$ $1$ ) $8x - 5y = 25$ $\newline$ $2$ ) $-2x + 7y = 11$ $\newline$ We aim to eliminate one variable by making the coefficients of $x$ or $y$ equal in both equations.
Multiply second equation: Step $2$ : Multiply the second equation by $4$ to align the coefficients of $x$ . $\newline$ Original second equation: $-2x + 7y = 11$ $\newline$ Multiply by $4$ : $-8x + 28y = 44$ $\newline$ Now, the equations are: $\newline$ $1$ ) $8x - 5y = 25$ $\newline$ $2$ ) $-8x + 28y = 44$
Add equations to eliminate x: Step $3$ : Add the two equations to eliminate x. $\newline$ $(8x - 5y) + (-8x + 28y) = 25 + 44$ $\newline$ $0x + 23y = 69$ $\newline$ Simplify: $y = \frac{69}{23}$ $\newline$ $y = 3$
Substitute to find $x$ : Step $4$ : Substitute $y = 3$ back into one of the original equations to find $x$ . Using the first equation: $8x - 5y = 25$ Substitute $y$ : $8x - 5(3) = 25$ $8x - 15 = 25$ $8x = 25 + 15$ $8x = 40$ $x = 40 / 8$ $y = 3$ $0$