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
[tex](y-5)+2y=1\\y-5+2y=1\\3y=1+5\\3y=6[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{6}{3}\\y=2[/tex]
Putting y=2 in Eqn 2
[tex]x=2-5\\x=-3[/tex]
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
[tex]3x-x=4\\2x=4[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{4}{2}\\x=2[/tex]
Putting x=2 in Eqn 2
[tex]y=3(2)\\y=6[/tex]
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
[tex]x=-x+2\\x+x=2\\2x=2[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{2}{2}\\x=1[/tex]
Putting x=1 in Eqn 1
[tex]y=1[/tex]
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
[tex]x+3(5x+4)=4\\x+15x+12=4\\16x=4-12\\16x=-8[/tex]
Dividing both sides by 16
[tex]\frac{16x}{16}=\frac{-8}{16}\\x=-0.5[/tex]
Putting x= -0.5 in Eqn 1
[tex]y=5(-0.5)+4\\y=-2.5+4\\y=1.5[/tex]
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
[tex]x-(3-x)=12\\x-3+x=12\\2x=12+3\\2x=15[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{15}{2}\\x=7.5[/tex]
Putting x=7.5 in Eqn 2
[tex]y=3-7.5\\y=-4.5[/tex]
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
[tex]2x+(5-x)=3\\2x+5-x=3\\x=3-5\\x=-2[/tex]
Putting x=-2 in Eqn 1
[tex]2(-2)+y=3\\-4+y=3\\y=3+4\\y=7[/tex]
The solution set is (-2,7).
Keywords: linear equation, substitution method
Learn more about substitution method at:
- brainly.com/question/9231234
- brainly.com/question/9214411
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