Solve the following pair of linear equations | vedclass

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(A) Given equations are:$(1) \frac{3x}{2} - \frac{5y}{3} = -2$$(2) \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$Step $1$: Simplify the equations.Multiply

Vedclass · Accepted Answer

$x = 2, y = 3$

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(A) Given equations are:$(1) \frac{3x}{2} - \frac{5y}{3} = -2$$(2) \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$Step $1$: Simplify the equations.Multiply $(1)$ by $6$: $9x - 10y = -12$  --- $(3)$Multiply $(2)$ by $6$: $2x + 3y = 13$  --- $(4)$Step $2$: Express $x$ in terms of $y$ from equation $(4)$:$2x = 13 - 3y$$x = \frac{13 - 3y}{2}$ --- $(5)$Step $3$: Substitute $(5)$ into $(3)$:$9(\frac{13 - 3y}{2}) - 10y = -12$Multiply by $2$: $9(13 - 3y) - 20y = -24$$117 - 27y - 20y = -24$$-47y = -24 - 117$$-47y = -141$$y = \frac{141}{47} = 3$Step $4$: Substitute $y = 3$ into $(5)$:$x = \frac{13 - 3(3)}{2} = \frac{13 - 9}{2} = \frac{4}{2} = 2$Thus,the solution is $x = 2, y = 3$.

Solve the following pair of linear equations by the substitution method:
$\frac{3x}{2} - \frac{5y}{3} = -2$
$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

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Solve the following pair of linear equations by the substitution method:$\frac{3x}{2} - \frac{5y}{3} = -2$$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$