Answer:
Step-by-step explanation:
A). Linear equation are x + y = -1 ----------(1)
and -6x + 2y = 14 ------(2)
First we multiply equation 1 by 6 then we add it to equation 2.
6(x + y) + (-6x + 2y) = -6 + 14
6x + 6y - 6x + 2y = 8
8y = 8
y = 1
By putting y = 1 in the equation 1
1 + x = -1
x = -1 -1 = -2
Solution will be (-2, 1)
B). Linear equations are x - 2y = -5 -----(1)
and 5x + 3y = 27 ------(2)
We multiply equation 1 by 5 and subtract it from 2
(5x + 3y) - 5(x - 2y) = 27 - 5(-5)
5x + 3y - 5x + 10y = 27 + 25
13y = 52
y = 4
By putting y = 4 in equation 1
x = -5 + 2y = -5 + 2(4)
= -5 + 8
= 3
solutions will be (3, 4)
C). -4x + y = -9 -----(1)
5x + 2y = 3 ----(2)
We multiply equation 1 by 2 and subtract it from equation 2
5x + 2y - 2(-4x + y) = 3 - 2(-9)
5x + 2y + 8x - 2y = 3 + 18
13x = 21
x = [tex]\frac{21}{13}[/tex]
By putting x = [tex]\frac{21}{13}[/tex] in equation 1
y = 9 + 4y
= 9 + 4([tex]\frac{21}{13}[/tex])
= 9 + [tex]\frac{84}{13}[/tex]
= [tex]\frac{201}{13}[/tex]
Solution will be [tex](\frac{21}{13}, \frac{201}{13})[/tex]
D). 6x + 3y = -6 ---- (1)
2x + y = -2 ------(2)
By multiplying equation 2 by (-3) and add it to equation 1
6x + 3y + (-3)(2x + y) = -6 + (-2)(-3)
6x + 3y - 6x - 3y = -6 + 6
0 = 0
Therefore, this equation has infinite solutions.
E). -x + 2y = 4 ----(1)
-3x + 6y = 11
3(-x + 2y) = 11
-x + 2y = [tex]\frac{11}{3}[/tex]-----(2)
So this system of linear equations has no solution.
F). -7x + y = 1 ---- (1)
14x - 7y = 28 -----(2)
We divide equation 2 by 7 and add it to the equation 1
-7x + y + 2x -y = 1 + 4
-5x = 5
x = -1
Now we put x = -1 in equation 1
-7(-1) + y = 1
7 + y = 1
y = 1 - 7
y = -6
So the solution will be (-1, -6)
