Example 2:Solve the simultaneous equations by elimination method3 2yx   x2y8,5 .

The given simultaneous equations are:

1. 3x + 2y = -8
2. 5x - y = 2

Step 1: Align the equations

To use the elimination method, we need to align the equations so that the x's and y's line up:

3x + 2y = -8 5x - y = 2

Step 2: Make the coefficients of y the same in both equations

To do this, we can multiply the second equation by 2:

3x + 2y = -8 10x - 2y = 4

Step 3: Add the two equations

Now, we can add the two equations together. The y terms will cancel out:

(3x + 2y) + (10x - 2y) = -8 + 4 13x = -4

Step 4: Solve for x

To solve for x, we divide both sides of the equation by 13:

x = -4/13

Step 5: Substitute x into the first equation

Now that we have a value for x, we can substitute it into the first equation to solve for y:

3(-4/13) + 2y = -8 -12/13 + 2y = -8 2y = -8 + 12/13 2y = -92/13

Step 6: Solve for y

To solve for y, we divide both sides of the equation by 2:

y = -46/13

So, the solution to the system of equations is x = -4/13 and y = -46/13.