Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
DifficultSolve the following pair of linear equations:
$152x - 378y = -74$
$-378x + 152y = -604$
$152x - 378y = -74$
$-378x + 152y = -604$
(N/A) Given equations are:
$(1)$ $152x - 378y = -74$
$(2)$ $-378x + 152y = -604$
Step $1$: Add the two equations:
$(152x - 378x) + (-378y + 152y) = -74 - 604$
$-226x - 226y = -678$
Divide by $-226$:
$x + y = 3$ --- $(3)$
Step $2$: Subtract equation $(2)$ from equation $(1)$:
$(152x - (-378x)) + (-378y - 152y) = -74 - (-604)$
$530x - 530y = 530$
Divide by $530$:
$x - y = 1$ --- $(4)$
Step $3$: Solve equations $(3)$ and $(4)$:
Adding $(3)$ and $(4)$: $2x = 4 \implies x = 2$
Subtracting $(4)$ from $(3)$: $2y = 2 \implies y = 1$
Thus,the solution is $x = 2, y = 1$.
$(1)$ $152x - 378y = -74$
$(2)$ $-378x + 152y = -604$
Step $1$: Add the two equations:
$(152x - 378x) + (-378y + 152y) = -74 - 604$
$-226x - 226y = -678$
Divide by $-226$:
$x + y = 3$ --- $(3)$
Step $2$: Subtract equation $(2)$ from equation $(1)$:
$(152x - (-378x)) + (-378y - 152y) = -74 - (-604)$
$530x - 530y = 530$
Divide by $530$:
$x - y = 1$ --- $(4)$
Step $3$: Solve equations $(3)$ and $(4)$:
Adding $(3)$ and $(4)$: $2x = 4 \implies x = 2$
Subtracting $(4)$ from $(3)$: $2y = 2 \implies y = 1$
Thus,the solution is $x = 2, y = 1$.
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