a. The solution set is (-3,2)
b. The solution set is (2,6)
c. The solution set is (1,1)
d. The solution set is (-0.5,1.5)
e. The solution set is (7.5, -4.5)
f. The solution set is (-2,7)
Step-by-step explanation:
a. x+2y=1 Eqn 1
x=y-5 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
Dividing both sides by 3
Putting y=2 in Eqn 2
The solution set is (-3,2).
b. y-x=4 Eqn 1
y=3x Eqn 2
Putting value of y from Eqn 2 in Eqn 1
Dividing both sides by 2
Putting x=2 in Eqn 2
The solution set is (2,6)
c. y = x Eqn 1
y = -x+2 Eqn 2
Putting value of y from Eqn 1 in Eqn 2
Dividing both sides by 2
Putting x=1 in Eqn 1
The solution set is (1,1)
d. y=5x+4 Eqn 1
x+3y=4 Eqn 2
Putting value of y from Eqn 1 in Eqn 2
Dividing both sides by 16
Putting x= -0.5 in Eqn 1
The solution set is (-0.5,1.5)
e. x-y=12 Eqn 1
y = 3-x Eqn 2
Putting value of y from Eqn 2 in Eqn 1
Dividing both sides by 2
Putting x=7.5 in Eqn 2
The solution set is (7.5, -4.5)
f. 2x+y=3 Eqn 1
x+y=5 Eqn 2
From Eqn 2;
y = 5-x
Putting in Eqn 1
Putting x=-2 in Eqn 1
The solution set is (-2,7).
Keywords: linear equation, substitution method
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