Solution:

Substitution Method

Solve the systems of linear equation in two variables by substitution method.

• x - y = 11 and y = 2x + 19

Substitute the first equation to the value of y which is the second equation.

• x - y = 11
• x - (2x + 19) = 11
• -x - 19 = 11
• -x = 11 + 19
• x = -30

Substitute the value of x into the second equation. Then, solve the equation.

• y = 2x + 19
• y = 2(-30) + 19
• y = -60 + 19
• y = -41

Elimination Method

Solve the systems of linear equation in two variables by elimination method.

• x - y = 11 and y = 2x + 19

Add the equation together.

• x - y = 11
• y = 2x + 19
• x = -30

Substitute the value of x to the first equation.

• x - y = 11
• (-30) - y = 11
• -y = 11 + 30
• y = -41

Check the values of the variables obtained by substituting to the linear equations in the system.

• x = -30 and y = -41

Equation 1:

• x - y = 11
• (-30) - (-41) = 11
• -30 + 41 = 11
• 11 = 11 ✔

Equation 2:

• y = 2x + 19
• (-41) = 2(-30) + 19
• -41 = -60 + 19
• -41 = -41 ✔

Answer:

• The two numbers are {-30, -41}.

P.S: I just put two methods in your question or your problem in your modules which is solving the systems of linear equations in two variables but I don't know what method you are looking for so I just put two methods.

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