Problem:

Directions: Solve each system of equations by elimination.

• x + y = 5 and x - y = 77

Solution:

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

• x + y = 5 and x - y = 77

Add the equation together.

• x + y = 5
• x - y = 77
• 2x = 82

Divide both sides of the equation by 2.

• 2x/2 = 82/2
• x = 41

Substitute the value of x to the first equation.

• x + y = 5
• (41) + y = 5
• y = 5 - 41
• y = -36

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

• x = 41 and y = -36

Equation 1:

• x + y = 5
• (41) + (-36) = 5
• 41 - 36 = 5
• 5 = 5 ✔

Equation 2:

• x - y = 77
• (41) - (-36) = 77
• 41 + 36 = 77
• 77 = 77 ✔

Answer:

• The two numbers are {41, -36}.

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