Use the method of elimination to find the sol | vedclass

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Question

(C) First,we multiply the equation $\frac{x}{4} + \frac{y}{3} = 2$ by $12$ to convert it into an equation with integer coefficients:$3x + 4y = 24$ ...

Vedclass · Accepted Answer

$(4, 3)$

Vedclass · Answer

(C) First,we multiply the equation $\frac{x}{4} + \frac{y}{3} = 2$ by $12$ to convert it into an equation with integer coefficients:$3x + 4y = 24$ .......... $(1)$$4x + 3y = 25$ .......... $(2)$To eliminate $x$,multiply equation $(1)$ by $4$ and equation $(2)$ by $3$:$12x + 16y = 96$ .......... $(3)$$12x + 9y = 75$ .......... $(4)$Subtracting equation $(4)$ from equation $(3)$:$(12x - 12x) + (16y - 9y) = 96 - 75$$7y = 21$$y = 3$Substituting $y = 3$ into equation $(1)$:$3x + 4(3) = 24$$3x + 12 = 24$$3x = 12$$x = 4$Thus,the solution is $(x, y) = (4, 3)$.

Use the method of elimination to find the solution of the following pair of linear equations: $\frac{x}{4} + \frac{y}{3} = 2, 4x + 3y = 25$.

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