Solution:

Substitution Method

Solve linear equations x - 3y = -8 and 2x + y = 5 using Substitution Method.

Solve for the value of x for the first equation.

• x - 3y = -8
• x = -8 + 3y

Substitute the expression for y into the second equation. Then, solve the equation.

• 2x + y = 5
• 2(-8 + y) + y = 5
• -16 + 7y = 5
• 7y = 5 + 16
• 7y = 21/7
• y = 3

Substitute the value into the value of y to the equation and solve.

• x = -8 + 3y
• x = -8 + 3(3)
• x = -8 + 9
• x = 1

Elimination Method

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

• x - 3y = -8 and 2x + y = 5

Add the equation together.

• x - 3y = -8
• 2x + y = 5
• 7y = 21

Divide both sides of the equation by 7.

• 7y/7 = 21/7
• y = 3

Substitute the value of y to the second equation.

• 2x + y = 5
• 2x + (3) = 5
• 2x = 5 - 3
• 2x = 2/2
• x = 1

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

• x = 1 and y = 3

Equation 1:

• x - 3y = -8
• (1) - 3(3) = -8
• 1 - 9 = -8
• -8 = -8 ✔

Equation 2:

• 2x + y = 5
• 2(1) + (3) =. 5
• 2 + 3 = 5
• 5 = 5 ✔

Answer:

• The two numbers are {1, 3}.

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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