3x - 4y = 10 ; 4x + 3y = 5

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Write Equations: Write down the system of equations to be solved. We have the system of equations: 3x - 4y = 10 4x + 3y = 5Eliminate y: Multiply the first equation by 4 and the second equation by 3 to eliminate y when we add the equations together. Multiplying the first equation by 4: 4 * (3x - 4y) = 4 * 10 12x - 16y = 40  Multiplying the second equation by 3: 3 * (4x + 3y) = 3 * 5 12x + 9y = 15Add Equations: Add the two new equations together to eliminate y. (12x - 16y) + (12x + 9y) = 40 + 15 24x - 7y = 55Solve for x: Solve the resulting equation for x. 24x = 55 + 7y x = (55 + 7y) / 24 Since we cannot simplify this further without knowing the value of y, we will use this expression for x in the next steps.Substitute for y: Substitute the expression for x back into one of the original equations to solve for y. We will use the first original equation: 3x - 4y = 10 Substitute x with (55 + 7y) / 24: 3 * ((55 + 7y) / 24) - 4y = 10 (165 + 21y) / 24 - 4y = 10Clear Fraction: Multiply through by 24 to clear the fraction. 24 * ((165 + 21y) / 24) - 24 * 4y = 24 * 10 165 + 21y - 96y = 240Solve for y: Combine like terms and solve for y. 165 - 75y = 240 -75y = 240 - 165 -75y = 75 y = 75 / -75 y = -1Substitute for x: Substitute the value of y back into the expression for x. x = (55 + 7y) / 24 x = (55 + 7(-1)) / 24 x = (55 - 7) / 24 x = 48 / 24 x = 2

$3x - 4y = 10 ; 4x + 3y = 5$

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3x−4y=10;4x+3y=53x - 4y = 10 ; 4x + 3y = 53x−4y=10;4x+3y=5

$3x - 4y = 10 ; 4x + 3y = 5$