Class 10MathematicsPair of Linear Equations in Two VariablesMix Examples - Pair of Linear Equations in Two Variables
MediumSolve the following pair of linear equations in two variables using a graph: $3x + 6y = 4$ and $2x + 4y = \frac{8}{3}$.
(D) Given equations are:
$1) 3x + 6y = 4$
$2) 2x + 4y = \frac{8}{3}$
Multiply equation $(2)$ by $\frac{3}{2}$:
$\frac{3}{2}(2x + 4y) = \frac{3}{2} \times \frac{8}{3}$
$3x + 6y = 4$
Since both equations represent the same line,they are coincident lines.
Therefore,the system has infinitely many solutions. The solution set is $\{(x, y) \mid 3x + 6y = 4; x, y \in R \}$.
$1) 3x + 6y = 4$
$2) 2x + 4y = \frac{8}{3}$
Multiply equation $(2)$ by $\frac{3}{2}$:
$\frac{3}{2}(2x + 4y) = \frac{3}{2} \times \frac{8}{3}$
$3x + 6y = 4$
Since both equations represent the same line,they are coincident lines.
Therefore,the system has infinitely many solutions. The solution set is $\{(x, y) \mid 3x + 6y = 4; x, y \in R \}$.
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