What system of linear equations in two variables equivalent to
Answers
Step-by-step explanation:
The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair [Math Processing Error] is the solution to the system of linear equations.
Answer:
Excellent question. When there are two variables, a system of equations (defined as more than one equation) looks like this:
x + y= 8
2x + 3y = 5
Step-by-step explanation:
- Systems of equations can be solved using a variety of techniques, such as graphing, elimination, and substitution.
- The simplest methods entail substitution or omission. Observe that there are no coefficients in front of the letters "x" or "y" in the first equation in the set above, "x + y = 8."
- It is crucial to choose which term to omit when comparing this to the equation below, "2x + 3y = 5," depending on whether it contains the letters "x" or "y." Let's decide to remove the "x" from both equations for our purposes.
- You must multiply the first equation by [-2] to achieve this.
- Why? The top term will become [-2x] when we multiply by [-2], and when we add [2x] to the bottom term, it will cancel out or "zero" out.
Let's test it, then:
-2 [x + y = 8] + 2x + 3y = 5
Formula 1: -2x - 2y = -16
Equation 2: 2x plus 3y equals 5.
One final equation is created by adding the two equations: [y = -11]
Great! You now have knowledge of one of the equations' variables. Replace the variable on either of the original equations with this: (I prefer the top one best; it requires less effort!)
Where y = -11, x Plus y equals 8.
x + (-11) = 8 <=== the equal sign with (11) added to both sides: x
x = 19.
The solution is x = 19, y = -11.
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