State whether the following statement is True or False. Justify your answer:
The coordinates of points in the table:
$x$$0$$1$$2$$3$$4$
$y$$2$$3$$4$$-5$$6$

represent some of the solutions of the equation $x-y+2=0$.

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(B) To determine if the points are solutions,we substitute the values of $x$ and $y$ into the equation $x-y+2=0$.
For $(0, 2)$: $0 - 2 + 2 = 0$. (True)
For $(1, 3)$: $1 - 3 + 2 = 0$. (True)
For $(2, 4)$: $2 - 4 + 2 = 0$. (True)
For $(3, -5)$: $3 - (-5) + 2 = 3 + 5 + 2 = 10 \neq 0$. (False)
For $(4, 6)$: $4 - 6 + 2 = 0$. (True)
Since the point $(3, -5)$ does not satisfy the equation,the statement is False.

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Similar Questions

Draw the graph of each of the equations given below. Also,find the coordinates of the points where the graph intersects the coordinate axes:
$1. 3x + 5y = 15$
$2. 5x - 2y = 10$
$3. 4x + 3y = -12$
$4. 3x - 7y = 21$
$5. x - y = 0$
$6. 2x - 3y = 0$
$7. x - y = -5$
$8. 5x - 3y = 15$

Write whether the following statements are True or False? Justify your answers.
$(i)$ The line parallel to the $y$-axis at a distance of $4$ units to the left of the $y$-axis is given by the equation $x = -4$.
$(ii)$ The graph of the equation $y = mx + c$ passes through the origin.

Show that the points $A(1, 2)$,$B(-1, -16)$,and $C(0, -7)$ lie on the graph of the linear equation $y = 9x - 7$.

Write the following equation in the standard form $ax + by + c = 0$ and indicate the values of $a, b,$ and $c$ in each case: $2x = 3y$.

Write whether the following statements are True or False? Justify your answers.
$(i)$ $ax + by + c = 0$,where $a, b$ and $c$ are real numbers,is a linear equation in two variables.
$(ii)$ $A$ linear equation $2x + 3y = 5$ has a unique solution.
$(iii)$ All the points $(2, 0), (-3, 0), (4, 2)$ and $(0, 5)$ lie on the $x$-axis.

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