Question

Please help me with 3 please

Answer 1

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

$(y-5)+2y=1\\y-5+2y=1\\3y=1+5\\3y=6$

Dividing both sides by 3

$\frac{3y}{3}=\frac{6}{3}\\y=2$

Putting y=2 in Eqn 2

$x=2-5\\x=-3$

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

$3x-x=4\\2x=4$

Dividing both sides by 2

$\frac{2x}{2}=\frac{4}{2}\\x=2$

Putting x=2 in Eqn 2

$y=3(2)\\y=6$

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

$x=-x+2\\x+x=2\\2x=2$

Dividing both sides by 2

$\frac{2x}{2}=\frac{2}{2}\\x=1$

Putting x=1 in Eqn 1

$y=1$

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

$x+3(5x+4)=4\\x+15x+12=4\\16x=4-12\\16x=-8$

Dividing both sides by 16

$\frac{16x}{16}=\frac{-8}{16}\\x=-0.5$

Putting x= -0.5 in Eqn 1

$y=5(-0.5)+4\\y=-2.5+4\\y=1.5$

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

$x-(3-x)=12\\x-3+x=12\\2x=12+3\\2x=15$

Dividing both sides by 2

$\frac{2x}{2}=\frac{15}{2}\\x=7.5$

Putting x=7.5 in Eqn 2

$y=3-7.5\\y=-4.5$

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

$2x+(5-x)=3\\2x+5-x=3\\x=3-5\\x=-2$

Putting x=-2 in Eqn 1

$2(-2)+y=3\\-4+y=3\\y=3+4\\y=7$

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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