Question

Solve the following pair of simultaneous equation
(1.) 5x+y=28 and x+y=2
(2.) 3m+n=10 and 5m-2n=2

Answer 1

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Given:

1. 5x + y = 28 and x + y = 2
2. 3m + n = 10 and 5m - 2n = 2

To Find:

• Solution of these equations

Solution:

1) 5x + y = 28 and x + y = 2

5x + y = 28 -----(i)

x + y = 2 ------(ii)

Subtract (ii) from (i),

=> 5x + y - (x + y) = 28 - 2

=> 5x - x + y - y = 26

=> 4x = 26

=> x = 26/4 = 13/2

=> y = 2 - x = 2 - 13/2 = (4-13)/2 = -9/2

Solution => x--> 13/2 & y--> -9/2

2) 3m + n = 10 and 5m - 2n = 2

3m + n = 10----(iii)

5m - 2n = 2----(iv)

Multiply (iii) by 2

=> 6m + 2n = 20----(v)

Add (iv) & (v),

=> 5m - 2n + 6m + 2n = 2 + 20

=> 5m + 6m - 2n + 2n = 22

=> 11m = 22

=> m = 22/11 = 2

=> n = 10 - 3m = 10 - 3(2) = 10 - 6 = 4

Solution => m--> 2 & n--> 4

Hope it helps!!

Answer 2

1) Answer:

X=13/2 and Y= -9/2

Step-by-step explanation:

5x+y=28,x+y=2

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

5x+y=28

Subtract y from both sides of the equation.

5x=−y+28

Divide both sides by 5.

x= 1/5 (−y+28)

Multiply 1/5 times −y+28.

x= -1/5y +28/5

Substitute -y+28/5 for x in the other equation, x+y=2.

-1/5y+28/5+y=2

Add -y/5 to y

4/5y28/5=2

Subtract  28/5 from both sides of the equation.

4/5y =-18/5

Divide both sides of the equation by  4/5, which is the same as multiplying both sides by the reciprocal of the fraction.

y=-9/2

Substitute -9/2 for y in x = -1/5y + 28/5. Because the resulting equation contains only one variable, you can solve for x directly.

x= -1/5(-9/2) + 28/5

Multiply − 1/5 times −9/2 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

x= 9/10 + 28/5

Add  28/5 to 9/10 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

x= 13/2

X=13/2 and Y= -9/2

2) Answer

m=2 and n=4

Step-by-step explanation:

Choose one of the equations and solve it for m by isolating m on the left hand side of the equal sign.

3m+n=10

Subtract n from both sides of the equation.

3m=−n+10

Divide both sides by 3.

m=1/3 (-n+10)

Multiply 1/3 times -n+10

m=-1/3n + 10/3

Substitute -n+10/3 for m in the other equation, 5m−2n=2.

5 (-1/3n + 10/3)-2n =2

Multiply 5 times -n +10/3

-5/3n + 50/3 -2n=2

Add -5n/3 to -2n

-11/3n + 50/3 =2

Subtract 50/3 from both sides of the equation.

-11/3n = -44/3

Divide both sides of the equation by -11/3, which is the same as multiplying both sides by the reciprocal of the fraction.

n=4

Substitute 4 for n in m= =1/3n + 10/3 Because the resulting equation contains only one variable, you can solve for m directly.

m = -1/3 * 4 +10/3

Multiply -1/3 times 4

m=-4+10/3

m= 2

m=2,n=4

Done!!

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