Stimulates equations

Example

Solve these simultaneous equations and find the values of x and y.

• Equation 1: 2x + y = 7
• Equation 2: 3x - y = 8

Add the two equations to eliminate the ys:

• 2x + y = 7
• 3x - y = 8
• 5x = 15
• x = 3

• Now you can put x = 3 in either of the equations.
• Substitute x = 3 into the equation 2x + y = 7:
• 6 + y = 7
• y = 1

So the answers are x = 3 and y = 1

Sometimes you will need to multiply one of the equations before you can add or subtract.

• Solve the two equations:
• Equation 1: 2a - 5b = 11
• Equation 2: 3a + 2b = 7

• 4a - 10b = 22 (Multiply by 2)
• 15a + 10b = 35 (Multiply by 5)
• ----------------------
• 19a = 57 (Adding)
• a = 3

• Put a = 3 into the equation 3a + 2b = 7:
• 9 + 2b = 7
• 2b = -2
• b = -1

So the answers are a = 3 and b = -1.

Solve the simultaneous equations:

Equation 1: y - 2x = 1

Equation 2: 2y - 3x = 5

Rearranging Equation 1, we get y = 1 + 2x

We can replace the 'y' in equation 2 by substituting it with 1 + 2x

Equation 2 becomes: 2(1 + 2x) - 3x = 5

2 + 4x - 3x = 5

2 + x = 5

x = 3

Substituting x = 3 into Equation 1 gives us y - 6 = 1, so y = 7.

Good luck revising