Solve the system of equations by substitution: 2x - y = -8 5x + y = 26

To solve the system of equations 2x - y = -8 and 5x + y = 26 using substitution, follow these steps:

Step 1: Solve one of the equations for one variable in terms of the other variable. It is usually easiest to solve for the variable that has a coefficient of 1 or -1. In this case, we can solve the first equation, 2x - y = -8, for y:

y = 2x + 8

Step 2: Substitute the expression found in Step 1 into the other equation. We will substitute 2x + 8 for y in the second equation, 5x + y = 26:

5x + (2x + 8) = 26

Step 3: Simplify the equation and solve for x:

5x + 2x + 8 = 26 7x + 8 = 26

Subtract 8 from both sides of the equation:

7x + 8 - 8 = 26 - 8 7x = 18

Divide both sides by 7:

7x / 7 = 18 / 7 x = 18 / 7 x = 2 4/7 or approximately 2.57

Step 4: Substitute the value of x back into the expression we found for y in Step 1:

y = 2(2 4/7) + 8

Convert 2 4/7 to an improper fraction to make the calculation easier:

y = 2(18/7) + 8 y = 36/7 + 8 y = 36/7 + 56/7 y = (36 + 56) / 7 y = 92 / 7 y = 13 1/7 or approximately 13.14

Step 5: Write down the solution as an ordered pair (x, y):

(2 4/7, 13 1/7) or approximately (2.57, 13.14)

This ordered pair is the solution to the system of equations, meaning that it satisfies both equations.