(A) Given equations are:$(1) x + 8y = 19$$(2) 2x + 11y = 28$From equation $(1)$,we can express $x$ in terms of $y$:$x = 19 - 8y$Substitute this value

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(A) Given equations are:$(1) x + 8y = 19$$(2) 2x + 11y = 28$From equation $(1)$,we can express $x$ in terms of $y$:$x = 19 - 8y$Substitute this value of $x$ into equation $(2)$:$2(19 - 8y) + 11y = 28$$38 - 16y + 11y = 28$$38 - 5y = 28$$-5y = 28 - 38$$-5y = -10$$y = 2$Now,substitute $y = 2$ back into the expression for $x$:$x = 19 - 8(2)$$x = 19 - 16$$x = 3$Thus,the solution is $(x, y) = (3, 2)$.

Class 10 Mathematics Pair of Linear Equations in Two Variables Mix Examples - Pair of Linear Equations in Two Variables

Medium

Solve the following pair of linear equations by the method of substitution: $x + 8y = 19$ and $2x + 11y = 28$.

A
$(3, 2)$
B
$(5, 7)$
C
$(4, 1)$
D
$(2, -1)$

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Solve the following pair of linear equations by the method of substitution: $x + 8y = 19$ and $2x + 11y = 28$.

Similar Questions

Half the perimeter of a rectangular garden,whose length is $4 \, m$ more than its width,is $36 \, m$. Represent this as a pair of linear equations in two variables.

The ratio of the present ages of Rajan and Jay is $3:2$. After five years,the ratio of their ages will be $4:3$. Find the present ages of both.

Solve the following pairs of equations by the method of elimination:$9x + 7y = 55$$7x + 9y = 57$

The equation $3x - 2y + 5 = 0$ can be written as:

Solve the following pairs of equations by the method of elimination:$7(y+3)-2(x+2)=14$$4(y-2)+3(x-3)=2$

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Solve the following pairs of equations by the method of elimination:
$9x + 7y = 55$
$7x + 9y = 57$

Solve the following pairs of equations by the method of elimination:
$7(y+3)-2(x+2)=14$
$4(y-2)+3(x-3)=2$