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There are always three ways to solve a system of equationsThere are three ways to solve systems of linear equations: substitution, elimination, and graphing. Let’s review the steps for each method. Substitution
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Graphing
Solving the same system with substitution, then with elimination, then with graphingTake the courseWant to learn more about Algebra 1? I have a step-by-step course for that. :)Determining which method is best for solving the system: substitution, elimination, or graphingNow let’s look at a few examples in which we need to decide which of these three methods to use. Example Which method would you use to solve the following problem? Explain why you picked the method that you did. ???x=y+2??? ???3y-2x=15??? The easiest way to solve this system would be to use substitution since ???x??? is already isolated in the first equation. Whenever one equation is already solved for a variable, substitution will be the quickest and easiest method. Even though you’re not asked to solve, these are the steps to solve the system: Substitute ???y+2??? for ???x??? in the second equation. ???3y-2(y+2)=15??? Distribute the ???-2??? and then combine like terms. ???3y-2y-4=15??? ???y-4=15??? Add ???4??? to both sides. ???y-4+4=15+4??? ???y=19??? Plug ???19??? for ???y??? into the first equation. ???x=y+2??? ???x=19+2??? ???x=21??? The unique solution is ???(21,19)???. There are three ways to solve systems of linear equations: substitution, elimination, and graphing. How to solve a system using the elimination methodExample To solve the system by elimination, what would be a useful first step? ???x+3y=12??? ???2x-y=5??? When we use elimination to solve a system, it means that we’re going to get rid of (eliminate) one of the variables. So we need to be able to add the equations, or subtract one from the other, and in doing so cancel either the ???x???-terms or the ???y???-terms. Any of the following options would be a useful first step: Multiply the first equation by ???-2??? or ???2???. This would give us ???2x??? or ???-2x??? in both equations, which will cause the ???x???-terms to cancel when we add or subtract. Multiply the second equation by ???3??? or ???-3???. This would give us ???3y??? or ???-3y??? in both equations, which will cause the ???y???-terms to cancel when we add or subtract. Divide the second equation by ???2???. This would give us ???x??? or ???-x??? in both equations, which will cause the ???x???-terms to cancel when we add or subtract. Divide the first equation by ???3???. This would give us ???y??? or ???-y??? in both equations, which will cause the ???y???-terms to cancel when we add or subtract. Let’s re-do the last example, but instead of the elimination method, use a graph to find the solution. Solving the system by graphing both equations and finding the intersection pointsExample Graph both equations to find the solution to the system. ???x+3y=12??? ???2x-y=5??? In order to graph these equations, let’s put both of them into slope-intercept form. We get ???x+3y=12??? ???3y=-x+12??? ???y=-\frac13x+4??? and ???2x-y=5??? ???-y=-2x+5??? ???y=2x-5??? The line ???y=-(1/3)x+4??? intersects the ???y???-axis at ???4???, and then has a slope of ???-1/3???, so its graph is The line ???y=2x-5??? intersects the ???y???-axis at ???-5???, and then has a slope of ???2???, so if you add its graph to the graph of ???y=-(1/3)x+4???, you get Looking at the intersection point, it appears as though the solution is approximately ???(3.75,2.75)???. In actuality, the solution is ???(27/7,19/7)\approx(3.86,2.71)???, so our visual estimate of ???(3.75,2.75)??? wasn’t that far off. Get access to the complete Algebra 1 courseLearn mathMay 4, 2019math, learn online, online course, online math, algebra, algebra 1, algebra i, algebra 2, algebra ii, solving systems, solving linear systems, systems of equations, systems of linear equations, substitution, solving with substitution, elimination, solving with elimination, graphing, solving by graphing, solving systems with substitution, solving systems with elimination, solving systems by graphing, substitution method, elimination method How do you solve system of equations by substitution?Here's how it goes:. Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for y: ... . Step 2: Substitute that equation into the other equation, and solve for x. ... . Step 3: Substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.. What are the 4 steps for solving systems of equations by elimination?Let's start our overview of how to solve a system of equations by elimination with a list of steps.. Determine which variable will be eliminated. ... . Combine the equations using addition. ... . Solve the new equation for the remaining variable.. Substitute the value for that variable into one of the original equations and solve.. What is substitution and elimination method?So, the major difference between the substitution and elimination method is that the substitution method is the process of replacing the variable with a value, whereas the elimination method is the process of removing the variable from the system of linear equations.
How do you solve with elimination?In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
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