Everything Maths Grade 10

Solving by elimination EMA3B

Worked example 8: Simultaneous equations

QUESTION

Solve the following system of equations:

3 x+y= 2 : : :(1)

6 xy= 25 : : :(2)

SOLUTION

Step 1: Make the coefficients of one of the variables the same in both equations

The coefficients ofyin the given equations are 1 and1. Eliminate the variableyby adding equation(1)and

equation(2)together:

3 x+y = 2

+ 6xy = 25

9 x+ 0 = 27

Step 2: Simplify and solve forx

9 x= 27

)x= 3

Step 3: Substitutexback into either original equation and solve fory

3 (3) +y= 2

y= 2 9

)y= 7

Step 4: Check that the solutionx= 3andy= 7 satisfies both original equations

Step 5: Write the final answer

x= 3

y= 7

84 4.4. Solving simultaneous equations