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Topic: **How to write a system of equations with 3 variables****Question:**
Ok so we learned how to solve the solution of the system using substitution. I don't uderstand it. How would you solve 6y+5x=8 and x+3y=-7. Please show steps and explain thoroughly. Like I really don't get how in the beginning you have to set up an equation using substitution. Please help(:

June 16, 2019 / By Abinoam

A system means that we know that an x in one equation means the same thing as the x in the other. If we only have one equation that has both an x and a y, it is impossible to know what the values are. There are an infinite number of combinations of x and y variables that can give you the constant on the right hand side of the equation. But with two equations, there will only be one x value and one y value that will be true for both cases. In algebra you can always move things around. a + b = c is that same as a + b - c = 0, and so on. We need to use both equations in order to find which values for x and y will satisfy both equations. So I always look for which variable is the easiest to isolate. In this case, isolating the x of the second equation is the easiest because it does not require any division: 6y + 5x = 8 x = -7 -3y By saying that the right hand side of the 2nd equation is equal to x, we can re-write the first equation using this "definition" of x: 6y + 5(-7 -3y) = 8 Now we have one equation with just one variable. We can solve for y: 6y -35 -15y = 8 -9y = 43 y = -43/9 Now that we have the y value, we can "plug it in" to either of our equations to find x. I will choose th 2nd because it looks easier: x + 3(-43/9) = -7 x - 43/3 = -7 x = 22/3 I hope this makes things slightly more clear. Another way of looking at it is to graph both linear equations. The solution is where the two lines meet. ie the two lines intersect at (22/3, -43/3)

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A system means that we know that an x in one equation means the same thing as the x in the other. If we only have one equation that has both an x and a y, it is impossible to know what the values are. There are an infinite number of combinations of x and y variables that can give you the constant on the right hand side of the equation. But with two equations, there will only be one x value and one y value that will be true for both cases. In algebra you can always move things around. a + b = c is that same as a + b - c = 0, and so on. We need to use both equations in order to find which values for x and y will satisfy both equations. So I always look for which variable is the easiest to isolate. In this case, isolating the x of the second equation is the easiest because it does not require any division: 6y + 5x = 8 x = -7 -3y By saying that the right hand side of the 2nd equation is equal to x, we can re-write the first equation using this "definition" of x: 6y + 5(-7 -3y) = 8 Now we have one equation with just one variable. We can solve for y: 6y -35 -15y = 8 -9y = 43 y = -43/9 Now that we have the y value, we can "plug it in" to either of our equations to find x. I will choose th 2nd because it looks easier: x + 3(-43/9) = -7 x - 43/3 = -7 x = 22/3 I hope this makes things slightly more clear. Another way of looking at it is to graph both linear equations. The solution is where the two lines meet. ie the two lines intersect at (22/3, -43/3)

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