Final answer:
To solve the first system using elimination, add the two equations together to eliminate the y terms. Solve for x and substitute the value into one of the equations to find y. For the second system, use the same method of elimination to solve for x and y.
Step-by-step explanation:
- For the first system, we use the method of elimination to solve. We can add the two equations together to eliminate the y terms. The result is 20x = -10. Dividing both sides by 20 gives us x = -0.5. Substituting this value back into one of the original equations, we find y = 5.
- For the second system, we again use the method of elimination. Adding the two equations together eliminates the y terms, giving us 4x = 3. Dividing both sides by 4 gives us x = 0.75. Substituting this value back into one of the original equations, we find y = 1.25.
Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.
Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3. In this article, we are going to discuss the definition of linear equations, standard form for linear equation in one variable, two variables, three variables and their examples with complete explanation.
An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true.