## What is the 4 steps in solving word problems?

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

- Step 1: Understand the problem.
- Step 2: Devise a plan (translate).
- Step 3: Carry out the plan (solve).
- Step 4: Look back (check and interpret).

## How do you solve simultaneous equations word problems?

solution

- Step 1: Make sure the equations have opposite x terms or opposite y terms.
- Step 2: Add to eliminate one variable and solve for the other.
- Step 3: Plug the result of Step 2 into one of the original equations and solve.
- Step 4: State the solution.

## How do you solve linear and quadratic simultaneous equations?

How to Solve using Algebra

- Make both equations into “y =” format.
- Set them equal to each other.
- Simplify into “= 0” format (like a standard Quadratic Equation)
- Solve the Quadratic Equation!
- Use the linear equation to calculate matching “y” values, so we get (x,y) points as answers.

## How do you solve simultaneous problems?

Example 2.

- Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient.
- Step 2: Subtract the second equation from the first.
- Step 3: Solve this new equation for y.
- Step 4: Substitute y = 2 into either Equation 1 or Equation 2 above and solve for x.

## Why do we need simultaneous equations?

Simultaneous equations are a system of equations that are all true together. You must find an answer or answers that work for all the equations at the same time. Simultaneous equations can be used to solve everyday problems, especially those that are more difficult to think through without writing anything down.

## What is the rule for simultaneous equations?

It works because of two properties of equations: Multiplying (or dividing) the expression on each side by the same number does not alter the equation. Adding two equations produces another valid equation: e.g. 2x = x + 10 (x = 10) and x − 3 = 7 (x also = 10).

## How do you solve simultaneous equations with 3 variables?

- Pick two pairs: 4x – 3y + z = – 10. 2x + y + 3z = 0.
- Eliminate the same variable from each system: 4x – 3y + z = – 10. 2x + y + 3z = 0.
- Solve the system of the two new equations: -5y – 5z = – 10. 5y – 7z = 34.
- Substitute into one of the original equations: – x + 2y – 5z = 17.
- Check: Does 2(1) + 4 + 3(- 2) = 0? Yes.

## How do you solve 3 variable equations quickly?

To use elimination to solve a system of three equations with three variables, follow this procedure:

- Write all the equations in standard form cleared of decimals or fractions.
- Choose a variable to eliminate; then choose any two of the three equations and eliminate the chosen variable.

## What is a root of an equation?

Roots are also called x-intercepts or zeros. The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.

## How do you find the real roots of an equation?

You can find the roots, or solutions, of the polynomial equation P(x) = 0 by setting each factor equal to 0 and solving for x. Solve the polynomial equation by factoring. Set each factor equal to 0. 2×4 = 0 or (x – 6) = 0 or (x + 1) = 0 Solve for x.

## How do you describe the roots of an equation?

The discriminant determines the nature of the roots of a quadratic equation. The word ‘nature’ refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary. If Δ≥0, the expression under the square root is non-negative and therefore roots are real.

## What does S stand for in motion?

In circumstances of constant acceleration, these simpler equations of motion are usually referred to as the SUVAT equations, arising from the definitions of kinematic quantities: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).

## What do you mean by free fall?

In Newtonian physics, free fall is defined as the motion of an object where gravity is the only force acting upon it. A skydiver may be pulled towards earth by gravity, but they are also affected by air resistance, a force opposing their downward movement.

## Which equation is known as position time equation?

Summary

traditional name | equation | relationship |
---|---|---|

1st equation | v = v0 + at | velocity-time |

2nd equation | s = s0 + v0t + ½at2 | position-time |

3rd equation | v2 = v02 + 2a(s − s0) | velocity-position |

merton rule | v = ½(v + v0) | average velocity |