Example of elimination method

Let's solve the following system of equations using the elimination method:

1) 2x + 3y = 11
2) 4x - 2y = 2

First, we need to choose a variable to eliminate. Let's eliminate y by multiplying the first equation by 2 and the second equation by 3:

1) 4x + 6y = 22
2) 12x - 6y = 6

Now, add the two equations together to eliminate y:

16x = 28

Divide both sides by 16 to solve for x:

x = 28/16
x = 7/4

Now, substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:

2(7/4) + 3y = 11
14/4 + 3y = 11
3y = 11 - 14/4
3y = 44/4 - 14/4
3y = 30/4
y = 10/4
y = 5/2

Therefore, the solution to the system of equations is x = 7/4 and y = 5/2.

Equation 1: 2x + 3y = 11
Equation 2: 4x - 5y = 1

Step 1: Multiply Equation 1 by 5 to make the coefficients of y the same.

5(2x + 3y) = 5(11)
10x + 15y = 55

Step 2: Add Equation 2 to the new Equation 1.

(10x + 15y) + (4x - 5y) = 55 + 1
14x + 10y = 56

Step 3: Solve for x.

14x = 56 - 10y
x = (56 - 10y) / 14
x = 4 - (5/7)y

Step 4: Substitute the expression for x in Equation 2 to solve for y.

4(4 - (5/7)y) - 5y = 1
16 - (20/7)y - 5y = 1
(112/7)y = 15
y = 15 - (7/112)
y = 15/16

Step 5: Substitute the value of y in the expression for x to find the exact value of x.

x = 4 - (5/7) - (15/16)
x = 4 - (75/112)
x = 112/112 - 75/112
x = 37/112

Therefore, the solution to the system of equations is x = 37/112 and y = 15/16.