(B) Given equations are:$1) 2x + y = 40$$2) x + y = 30$Subtracting equation $(2)$ from equation $(1)$:$(2x + y) - (x + y) = 40 - 30$$x = 10$Substituti

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(B) Given equations are:$1) 2x + y = 40$$2) x + y = 30$Subtracting equation $(2)$ from equation $(1)$:$(2x + y) - (x + y) = 40 - 30$$x = 10$Substituting $x = 10$ in equation $(2)$:$10 + y = 30$$y = 20$So,the solution is $(x, y) = (10, 20)$.Now,substitute these values into the equation $y = mx + 6$:$20 = m(10) + 6$$20 - 6 = 10m$$14 = 10m$$m = \frac{14}{10} = 1.4$.

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

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Solve the pair of linear equations $2x + y = 40$ and $x + y = 30$. If the solution satisfies the equation $y = mx + 6$,find the value of $m$.

A
$m = 1$
B
$m = 1.4$
C
$m = 2$
D
$m = 0.5$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

Draw the graphs of the lines $x=-2$ and $y=3$. Write the vertices of the figure formed by these lines,the $x$-axis and the $y$-axis. Also,find the area of the figure.

Medium

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Which of the following groups matches the data of Part $I$ with the data of Part $II$?

Part $I$ Part $II$

$1. x+2y=3, 2x+4y=5$ $a. \text{Solution set is a singleton set.}$

$2. 2x+3y=6, x+\frac{3}{2}y=3$ $b. \text{Solution set is an empty set.}$

$3. 3x-y=0, x-y+6=0$ $c. \text{Solution set is an infinite set.}$

$d. \text{Solution set contains two members.}$

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For which values of $p$ and $q$ will the following pair of linear equations have infinitely many solutions?
$4x + 5y = 2$
$(2p + 7q)x + (p + 8q)y = 2q - p + 1$

Difficult

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Determine,graphically,the vertices of the triangle formed by the lines $y=x$,$3y=x$,and $x+y=8$.

Difficult

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The solution of the pair of equations $x + 2y = 5$ and $2x + y = 4$ is .........

Easy

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Part $I$	Part $II$
$1. x+2y=3, 2x+4y=5$	$a. \text{Solution set is a singleton set.}$
$2. 2x+3y=6, x+\frac{3}{2}y=3$	$b. \text{Solution set is an empty set.}$
$3. 3x-y=0, x-y+6=0$	$c. \text{Solution set is an infinite set.}$
	$d. \text{Solution set contains two members.}$

Solve the pair of linear equations $2x + y = 40$ and $x + y = 30$. If the solution satisfies the equation $y = mx + 6$,find the value of $m$.

Similar Questions

Draw the graphs of the lines $x=-2$ and $y=3$. Write the vertices of the figure formed by these lines,the $x$-axis and the $y$-axis. Also,find the area of the figure.

For which values of $p$ and $q$ will the following pair of linear equations have infinitely many solutions?$4x + 5y = 2$$(2p + 7q)x + (p + 8q)y = 2q - p + 1$

Determine,graphically,the vertices of the triangle formed by the lines $y=x$,$3y=x$,and $x+y=8$.

The solution of the pair of equations $x + 2y = 5$ and $2x + y = 4$ is .........

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For which values of $p$ and $q$ will the following pair of linear equations have infinitely many solutions?
$4x + 5y = 2$
$(2p + 7q)x + (p + 8q)y = 2q - p + 1$