Algebra 1 Section 7.2

Solving a System by Graphing This works well only if the coordinates of the solution are small integers. Another method should be used if the solutions contain large integers or fractions.

Substitution Method This is used to find a single variable equation by replacing one of the variables with an equivalent expression.

Substitution Method Once this equation is solved, the result is substituted into one of the equations to find the value of the other variable.

Example 1 x + y = 5 y = -3x + 7 x + (-3x + 7) = 5 -2x + 7 = 5 -2x = -2

Example 1 Since we know that x = 1... y = -3x + 7 y = -3(1) + 7 y = 4 Solution: (1, 4)

Example 2 x + y = -4 x – y = 10 x = -y – 4 (-y – 4) – y = 10

Example 2 Since we know that y = -7... x = -y – 4 x = -(-7) – 4 x = 3 Solution: (3, -7)

Solving a System by Substitution Solve either equation for either variable. Choose the easiest variable to solve for. Substitute the solution into the other equation to obtain an equation in one variable; then solve.

Solving a System by Substitution Use the value of the known variable to solve for the other variable. Write the solution as an ordered pair.

Solving a System by Substitution Check the solution by substituting it into each equation.

Example 3 Note here that the “easiest” variable to solve for is x in the first equation: x = 4y. 3(4y) + 2y = 8

Example 4 You need to write two equations involving l, the length, and w, the width. We are told the length is 6 ft longer than the width. l = w + 6

Example 4 The perimeter formula helps us to get the other equation: 2l + 2w = 84 Since we know that l = w + 6... 2(w + 6) + 2w = 84

Example 4 2(w + 6) + 2w = 84 2w + 12 + 2w = 84 4w + 12 = 84 4w = 72 l = w + 6 l = 18 + 6 l = 24 width = 18 ft length = 24 ft

Homework: pp. 286-287