Systems of Linear Equations (3E3U): Method 1: Elimination by Substitution (1 of 4)

Systems of first-degree or linear equations: Three equations, Three unknowns (1 of 4). Method 1: Elimination by substitution.

The three given equations:
(1) u - 7v - 5w = 35,
(2) 3u + v + 10w = -12, and
(3) 2u - 6v + w = 37.

The three unknowns to solve for the values of, are the variables: u, v, and w.

To start solving using this method, inspect first the three given equations with three variables each, u, v, and w, which among them is the simplest to isolate. By inspection, u is the one which is the simplest among them in equation 1. Isolate u by transposing the two terms with v and w or u = 7v + 5w + 35, label it as eq. 1.1. Now substitute eq. 1.1 to eq. 2 making v = (-25w - 117)/22, label it as eq. 2.1. Substitute eq. 1.1 to eq. 3 making v = (-11w - 33)/8, label it as eq. 3.1. Equate equations 2.1 and 3.1 to solve for the value of w. At this point, the value of w is now solved, substitute its value to eq. 3.1 to solve for the value of v. At this point, the values of v and w are now solved. Substitute their values of to eq. 1.1 to solve for the value of u. The values of u, v, and w are now solved at this point.

To check if the values of u, v, and w are correct, substitute their values to the given three equations above.

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