Answer :
The simplification of given equation can be carried out by using slope intercept form and also by using the arithmetic operations.
1).
Given :
[tex]y = \dfrac{3}{4}x-7[/tex] --- (1)
To determine the slope of the given line, slope intercept form can be use and the slope intercept form is given by:
[tex]y = mx+c[/tex] --- (2)
Now, compare both the equation (1) and (2), we get the slope of the line [tex]y = \dfrac{3}{4}x-7[/tex] that is, [tex]m = \dfrac{3}{4}[/tex] .
2).
Given :
3y + 4x = 15
Further simplify the given equation.
[tex]y = \dfrac{-4x+15}{3}=\dfrac{-4}{3}x+5[/tex] ----- (3)
To determine the y-intercept of the given line, slope intercept form can be use and the slope intercept form is given by:
[tex]y = mx+c[/tex] --- (4)
Now, compare both the equation (3) and (4), we get the y-intercept of the line [tex]y = \dfrac{-4}{3}x+5[/tex] that is, [tex]c = 5[/tex].
3).
Given :
[tex]x = -4y[/tex] ---- (5)
[tex]x+5y = 2[/tex] ---- (6)
Now, substitute the value of 'y' given in equation (5) in equation (6).
[tex]-4y+5y=2[/tex]
[tex]y = 2[/tex]
Now, put the value of y in equation (5).
[tex]x = -4\times2[/tex]
[tex]x = -8[/tex]
Therefore, the correct option is A).
4).
Given :
3x + 4y = 31 ---- (7)
2x - 4y = -6 ---- (8)
Further simplify the equation (7).
[tex]x = \dfrac{31-4y}{3}[/tex] --- (9)
Now, put the value of x given in equation (9) in equation (8).
[tex]2\times\left[\dfrac{31-4y}{3}\right]-4y=-6[/tex]
[tex]62-8y-12y=-18[/tex]
62 - 20y = -18
80 = 20y
y = 4
Put the value of y in equation (9) we get:
x = 5
Therefore, the correct option is B).
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