Class 10MathematicsPair of Linear Equations in Two VariablesMix Examples - 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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Similar Questions
Which of the following groups truly matches the data of Part $I$ with the data of Part $II$?
Part $I$ Part $II$ $1.$ The solution of $2x - y = 4$ and $3x - 2y = 5$ $a.$ $x = 3, y = 2$ $2.$ The solution of $5x - y = 14$ and $4x - 3y = 9$ $b.$ $x = 3, y = 1$ $3.$ The solution of $4x - 3y = 5$ and $3x - y = 5$ $c.$ $x = 2, y = 1$ $4.$ The solution of $3x - 2y = -1$ and $2x - 5y = -8$ $d.$ $x = 1, y = 2$
| Part $I$ | Part $II$ |
| $1.$ The solution of $2x - y = 4$ and $3x - 2y = 5$ | $a.$ $x = 3, y = 2$ |
| $2.$ The solution of $5x - y = 14$ and $4x - 3y = 9$ | $b.$ $x = 3, y = 1$ |
| $3.$ The solution of $4x - 3y = 5$ and $3x - y = 5$ | $c.$ $x = 2, y = 1$ |
| $4.$ The solution of $3x - 2y = -1$ and $2x - 5y = -8$ | $d.$ $x = 1, y = 2$ |
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