Solving linear equations in twoPresentation Transcript
A first degree equation is called a linear equation in two variables if it contains two distinct variables.
1. Arbitrarily select some points that satisfy the equation.
2. Plot the points in a coordinate plane.
3. Draw the line passing through these points. This is the graph of the equation.
Graph y = 2x + 3.
Plotting the x-intercept and y-intercept of a graph and drawing a line through them is called the intercept method of graphing a linear equation.
Graph y = 2x + 4.
Set of two or more equations is called a system of equations .
Consider the following system of equations:
y – 2x = –6
y + x = –3
To solve the system, we can first graph each equation.
In order to solve a system of equations we can write the equations in a way that eliminates one of the unknowns. Then the remaining equality will be in one unknown, and we can solve this easily. This method is called the elimination method.
1. Write the given equations in the form Ax + By = C.
2. Take one equation. Make the coefficient of the variable which you want to eliminate the additive inverse of the same variable in the other equation.
3. Add the resulting equations to eliminate your chosen variable.
4. Solve the resulting equation in one unknown.
5. Find the other variable by substituting this solution into either original equation.
6. Check your result.
Another method for solving systems of equations is the substitution method.
1. Solve one of the equations for one variable in terms of the other variable.
2. Substitute the resulting expression into the other equation and solve.
3. Find the other variable by substituting the result of step 2 into either original equation.