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If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Video transcriptIs negative 1 comma 7 a solution for the system of linear equations below? And they give us the first equation is x plus 2y is equal to 13. Second equation is 3x minus y is equal to negative 11. In order for negative 1 comma 7 to be a solution for the system, it needs to satisfy both equations. Or another way of thinking about it, x equals 7, and y-- sorry, x is equal to negative 1. This is the x coordinate. X equals negative 1, and y is equal to 7, need to satisfy both of these equations in order for it to be a Solution. So let's try it out. Let's try it out with the first equation. So we have x plus 2y is equal to 13. So if we're thinking about that, we're testing to see if when x is equal to negative 1, and y is equal to 7, will x plus 2y equals 13? So we have negative 1 plus 2 times 7-- y should be 7-- this needs to be equal to 13. And I'll put a question mark there because we don't know whether it does. So this is the same thing as negative 1 plus 2 times 7 plus 14. That does, indeed, equal 13. Negative 1 plus 14, this is 13. So 13 does definitely equal 13. So this point it does, at least, satisfy this first equation. This point does sit on the graph of this first equation, or on the line of this first equation. Now let's look at the second equation. I'll do that one in blue. We have 3 times negative 1 minus y, so minus 7, needs to be equal to negative 11. I'll put a question mark here because we don't know whether it's true or not. So let's see, we have 3 times negative 1 is negative 3. And then we have minus 7 needs to be equal to negative 11-- I put the question mark there. Negative 3 minus 7, that's negative 10. So we get negative 10 equaling negative 11. No, negative 10 does not equal a negative 11. So x equaling negative 1, and y equaling 7 does not satisfy the second equation. So it does not sit on its graph. So this over here is not a solution for the system. So the answer is no. It satisfies the first equation, but it doesn't satisfy the second. In order to be a solution for the system, it has to satisfy both equations.
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What are systems of equations?A system of equations is a set of one or more equations involving a number of variables.The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect. To solve a system is to find all such common solutions or points of intersection. Systems of linear equations are a common and applicable subset of systems of equations. In the case of two variables, these systems can be thought of as lines drawn in two-dimensional space. If all lines converge to a common point, the system is said to be consistent and has a solution at this point of intersection. The system is said to be inconsistent otherwise, having no solutions. Systems of linear equations involving more than two variables work similarly, having either one solution, no solutions or infinite solutions (the latter in the case that all component equations are equivalent). More general systems involving nonlinear functions are possible as well. These possess more complicated solution sets involving one, zero, infinite or any number of solutions, but work similarly to linear systems in that their solutions are the points satisfying all equations involved. Going further, more general systems of constraints are possible, such as ones that involve inequalities or have requirements that certain variables be integers. Solving systems of equations is a very general and important idea, and one that is fundamental in many areas of mathematics, engineering and science. How do you find the solution to the system of equations without graphing?To solve a system of linear equations without graphing, you can use the substitution method. This method works by solving one of the linear equations for one of the variables, then substituting this value for the same variable in the other linear equation and solving for the other variable.
How do you find the solution to the system of equations on a graph?To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.
What does it mean to find the solution to a system?If you have a system of equations that contains two equations with the same two unknown variables, then the solution to that system is the ordered pair that makes both equations true at the same time. Follow along as this tutorial uses an example to explain the solution to a system of equations!
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How do you find a solution to a system of equation?
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