Use substitution method to work out the values of x and y in the simultaneous equation:

5x + 2y = 19

2x - 4y = - 2

Powered by Froala Editor

We are given the system of equations:

5x+2y = 19

2x−4y= - 2

Step 1: Use substitution method

We will solve one equation for one variable and substitute into the other.

Let’s solve Equation 1 for y:

5x + 2y = 19 

2y = 19 − 5x

y = 19 − 5x

           2

Step 2: Substitute into the second equation

Substitute 

y = 19 − 5x

           2

into the second equation:

2x − 4y = -2

2x − 4 (19−5x) = -2

                2

Simplify:

2x − 2(19−5x) = −2

2x − (38 − 10x) = −2

2x − 38 + 10x = −2

12x − 38 = −2

12x = 36

x = 3

Step 3: Substitute x = 3 into the expression for y

y = 19−5(3)

          2

y = 19−15 =  4 

          2           2

Final Answer:

x = 3 , y = 2

Powered by Froala Editor