Question

of Equations There are generally two approaches to solving systems of equations in physics, the substitution method and the addition method. Let us consider the system of two equations below: 4x + 2y 14 2x -y-1 We can solve these equations using both methods. First, the substitution method. The process is as follows: In one of the equations, solve for one of the variables . te this expression for that variable into the other equation. This will leave an expression that only depends on 1 variable. Solve for the missing variable Use this result in your expression for the variable you substitut ed. For the example provided, we first determine y: Next, we substitute this into our first expression and simplify Finally, we put this back into our expression for y: To use the addition method, we use the following procedure: y 2x -1-2(2)-1-3 Multiply both sides of an equation so that the coefficient of one of the variables is the same as in the other equation Add or subtract the two equations term by term, canceling out one of the variables Solve for the remaining variable Use this result in either expression to solve for the variable that canceled out previously e . . . In the example given, we can either multiply the first expression by 1/2 or the second expression by 2. Let's do the latter: 4x + 2y 14 4x-2y 2 We can see that if we add these two equations that 2y - 2y 0, canceling out the y terms! If we add expressions, we get which is the same result we got previously. We can use this result in either expression to determine that Activity 1-7: Solving Systems of Equations 1. Use the addition method to solve: 17a + 2-7b 2. Use the substitution method to solve: 2x+t+3 0 3. Use either method to sol y-2 4. Solve for x, y, & z using either method:2x-y+z 3 method to solve: 3t + 2 = 0 2x +3y 0

Answer 1