Answer:
(Q.1) No solution
(Q.2) True
(Q.3) x = 4 - 2y
(Q.4) True
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Explanation:
(Q.1) As shown in the first attached figure.
By graphing. x + 2y = 8 & x + 2y = -4
The two lines are parallel, there is no intersection points between the lines.
So, there is no solution to the system of equations.
Also, we should note the parallel lines have the same slope
to find it make the equation similar to y = mx + c where m is the slope
at this situation m = -1/2
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(Q.2) As shown in the second attached figure.
By graphing the system of inequalities y> -3x+2 & y<2x+1
The Shaded area represents the solution of the system of inequalities
And the point (4,2) is inside the shaded area
So, The ordered pair (4,2) is a solution to the system of inequalities.
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(Q.3) solving the system { x+2y=4 & 2x+2y=6 } by substitution
From the first equation x + 2y = 4
we will find x in terms of y then plug it into the second equation
So, x + 2y = 4 ⇒ x = 4 - 2y
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(Q.4) As shown in the third attached figure.
By graphing. 2x + 4y = 8 & x + 2y = 6
The two lines are parallel, there is no intersection points between the lines.
So, there is no solution to the system of equations.
Also, we should note the parallel lines have the same slope
to find it make the equation similar to y = mx + c where m is the slope
at this situation m = -1/2