{:[4x+5y=12],[5x+7y=14]:} solve for y

Write Equations: Write down the system of equations. We have the following system of equations: 4x + 5y = 12 5x + 7y = 14 We need to solve for y.Eliminate x: Multiply the first equation by 5 and the second equation by 4 to eliminate x. Multiplying the first equation by 5: (5)(4x) + (5)(5y) = (5)(12) 20x + 25y = 60 Multiplying the second equation by 4: (4)(5x) + (4)(7y) = (4)(14) 20x + 28y = 56Subtract Equations: Subtract the second new equation from the first new equation to eliminate x. (20x + 25y) - (20x + 28y) = 60 - 56 20x + 25y - 20x - 28y = 4 The 20x terms cancel out, and we are left with: 25y - 28y = 4Combine Terms: Combine like terms to solve for y. 25y - 28y = -3y So we have: -3y = 4Solve for y: Divide both sides by -3 to solve for y. y = 4 / (-3) y = -4/3

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$\begin{array}{l} 4 x+5 y=12 \\ 5 x+7 y=14 \end{array}$ $\newline$ solve for $y$

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\begin{array}{l} 4 x+5 y=12 \\ 5 x+7 y=14 \end{array}

\newline

solve for

y

Write Equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $4x + 5y = 12$ $\newline$ $5x + 7y = 14$ $\newline$ We need to solve for $y$ .
Eliminate x: Multiply the first equation by $5$ and the second equation by $4$ to eliminate $x$ . $\newline$ Multiplying the first equation by $5$ : $\newline$ $(5)(4x) + (5)(5y) = (5)(12)$ $\newline$ $20x + 25y = 60$ $\newline$ Multiplying the second equation by $4$ : $\newline$ $(4)(5x) + (4)(7y) = (4)(14)$ $\newline$ $20x + 28y = 56$
Subtract Equations: Subtract the second new equation from the first new equation to eliminate $x$ . $\newline$ $(20x + 25y) - (20x + 28y) = 60 - 56$ $\newline$ $20x + 25y - 20x - 28y = 4$ $\newline$ The $20x$ terms cancel out, and we are left with: $\newline$ $25y - 28y = 4$
Combine Terms: Combine like terms to solve for $y$ . $25y - 28y = -3y$ So we have: $-3y = 4$
Solve for y: Divide both sides by $-3$ to solve for y. $\newline$ $y = \frac{4}{(-3)}$ $\newline$ $y = -\frac{4}{3}$