# Solving Systems Of Equations Using Substitution

**Solving Systems Of Equations Using Substitution** – Download the free Solving Systems of Equations by Substitution worksheet and other teaching and understanding resources Solving Systems of Equations by Substitution

Solving a system of equations by substitution is a method for solving a system of two linear equations. Solving a system of equations by substitution follows a certain process to simplify the solutions. The first thing to do when solving systems of equations by substitution is to solve the equation for either variable. Then you must take the solution for the variable and replace it with another equation for the variable. Then you solve for the variable and get a numerical solution. Use the solution variable to substitute into any of the original equations. The last step in learning to solve a system of equations by substitution is to solve for the last variable following the order of operations.

## Solving Systems Of Equations Using Substitution

Solving a system of equations by substitution is a technique for explaining a set of two equations. The first thing to do when solving systems of equations by substitution is to solve the mathematical statement for any variable. Then you must take the answer for the variable and replace it with another mathematical statement for the variable. At that point you simplify the variable and get a numerical answer. Use a simplified variable to return the first or second math statement. The last part in solving a system of equations by substitution is to simplify for the last variable following the rules for the order of operations.

### Ways To Solve Systems Of Equations

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#### Solved Solve The System Of Linear Equations By Using

Here we are at the first problem. Anytime you try to solve a system of equations, your answer should be in the form of an X and an i-coordinate. This means that every time you solve it in any way, whether it’s graphing with subtraction or substitution, you must have a coordinate as the answer.

Here we will find our first problem for solving a system of equations by substitution. We have 3x minus and equal to 7, and then it’s equal to 2x plus 2. Now when you solve systems by substitution, you have to use substitution to replace one equation with another equation. In the case of this first problem, our second equation here is already solved for the variable I. We already know that I is equal to 2x plus 2 because it’s already been solved for i. We can take 2x + 2 and we can replace it with I in the second equation. What we’re going to do is we’re going to take our equation above and rewrite it into our second equation substituting it here. We have another equation 2x + 2 and we know that I is equal to that.

We changed it to where it was And now we have to solve for X. That means we have to simplify it. We’ll go ahead and distribute this negative to everyone inside the brackets. Now we have 3x minus 2x minus 2 because we’re doing minus 1 times 2x and then minus 1 times 2 is equal to 7. Now the next step is to combine like terms. We do 3x minus 2x and 3x minus 2x is 1/x. You take away your -2 and your 7, and then we’re going to add 2 to both sides, so we’re going to cancel that out as well and we’re going to have 1x or k is equal to 9.

### Solving A System Using Substitution

Now we know that X is equal to 9 and you remember that you have to have X and the i-coordinate. We take our Xs equal to 9 and we’ll substitute that back into Xs in our equation below. We’re going to take i equals 2 times our k value which is 9 plus 2 and is equal to 2 times 9 which is 18 plus 2. And is equal to 18 plus 2 which is 20. Now our complete solution is k equals 9. our k coordinate is 9, and then our coordinate is 20. We will use X is 9 and is 20 and that is the coordinate that is our solution.

The next problem we’re going to tackle in our system in our systems of equations using the substitution worksheet is the number 3. Now this time we have negative k plus 3i equals 3 and then the second equation is X minus 2i equals 8. Now this time we don’t have resolved variables. What we need to do is pick the variable we’re going to solve for when it’s solved, so we can replace it with another equation. You can solve for any variable, it’s up to you. You can solve this you can solve for this I, you can solve this X or you can solve this 2i. The easiest way to solve this is the X below because all you have to do is add the 2i to both sides and they will cancel out and you’ll automatically solve for k.

Now we know that X is equal to these two terms if we tried to solve for any other variable we would have a coefficient here and we would have to divide everything by that coefficient. This is the easiest variable to solve. We know that k is equal to 2i plus 8, we need to take this 2i plus 8 and we need to substitute it into our second equation or the equation above in this case. When we do that, we’re going to get our equation minus k or in this case minus 2i plus 8 because that’s what we’re substituting, and then plus 3i. We carry the rest. Now we know this is equal to minus 2i plus 8. We take this minus and distribute it over everything inside the parentheses. This is going to be minus 2i minus 1 times 8 minus 8 plus 3i is equal to 3. The next step is to combine like terms so that we add these two minus 2i plus 3i is 1i. You write down your minus 8, and then you write down your equal to 3. Then we have to add the 8 to both sides, and you get an I. Only 1i or i is equal to 11.

#### Solving Systems Of Linear Equations Using The Substitution Method

We know that I is equal to 11, so now we’re going to take i which is equal to 11 and we’re going to substitute 11 in for I back into the equation that we simplified for X. We have k equals 2 times that we know that I is 11 so we’re going to replace 11 with i plus 8 2 times 11 is 22 plus 8. And then when you solve for 22 plus 8 you get 30. The solution because we have to have coordinates like k equals 30 and is 11 and that is our total solution.v

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#### Systems Of Equations Inb Pages

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## Systems Of Equations Activities For Your Classroom

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In this section we will define a fully algebraic method for solving the system. The idea is to solve one

## Solving Linear Systems With Substitution

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