Question

SOLVE THE FOLLOWING PAIRS OF SIMULTANEOUS EQUATIONS: 1. 5A-2B = 14 AND 2A + 2B = 14 2. X+Y=4 AND 2X-Y =5​

Answer 1

To solve the simultaneous equations:
5A - 2B = 14 (Equation 1)
2A + 2B = 14 (Equation 2)
We can solve for one of the variables, say B, and substitute the resulting expression into one of the equations to solve for the other variable. Here's how:

From Equation 2, we can isolate B by subtracting 2A from both sides:
2A + 2B = 14
2B = 14 - 2A
B = (14 - 2A) / 2
B = 7 - A (Equation 3)

Now we can substitute Equation 3 into Equation 1 to get an equation in terms of A:
5A - 2B = 14
5A - 2(7 - A) = 14
5A - 14 + 2A = 14
7A = 28
A = 4

Substituting A = 4 into Equation 3 gives:
B = 7 - A
B = 7 - 4
B = 3

Therefore, the solution to the simultaneous equations is A = 4 and B = 3.

To solve the simultaneous equations:
X + Y = 4 (Equation 1)
2X - Y = 5 (Equation 2)
We can again solve for one of the variables and substitute the resulting expression into one of the equations to solve for the other variable. Here's how:

From Equation 1, we can isolate Y by subtracting X from both sides:
Y = 4 - X (Equation 3)

Now we can substitute Equation 3 into Equation 2 to get an equation in terms of X:
2X - Y = 5
2X - (4 - X) = 5
3X = 9
X = 3

Substituting X = 3 into Equation 3 gives:
Y = 4 - X
Y = 4 - 3
Y = 1

Therefore, the solution to the simultaneous equations is X = 3 and Y = 1

Answer 2

Answer: 1. A= 4 , B=3

2. X=3, Y= 1

Explanation:

1. Given: 5A-2B=14 - (a)

2A+2B=14 - (b)

To Find: A=? , B=?

Solution : Multiply Equation (a) by 2 and Equation (b) by 5 . Then we have ,

10A-4B=28 -(c)

10A+10B=70-(d)

Now subtract Equation (d) by Equation (c), We get

10A+10B=70

-( 10A-04B=28)

- + -

___________

0A+14B=42

___________

We get ,

B= 3

Put the value of B in Equation (a),

5A-2(3)=14

5A-6 = 14

5A = 20

A= 4

2. Given : X+Y=4 - (a)

2X-Y=5 - (b)

To Find: X=?, Y=?

Solution: Multiply Equation (a) by 2 , then we have

2X+2Y=8-(c)

Now subtract Equation (c) by (b) ,

2X+2Y=8

-(2X-1Y)=5

- + -

__________

0X+3Y=3

__________

Now , we have

3Y=3

Y=1

Put the value of Y in Equation (a),

X+1=4

X=3

Answer : 1. A= 4 , B=3

2. X=3, Y= 1