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Help me with this!?!

In order to solve a system by substitution, you want to...

get opposite coefficients for each variable in each equation.

get opposite coefficients for one set of variables in each equation.

isolate a variable in an equation and then substitute into the other equation.

put the corresponding augmented matrix into RREF (row reduced echelon form).

User Ganj Khani
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1 Answer

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Answer:

Explanation:

1. Solve one of the equations for one of the variables. For example, if the system is:

x + 2y = 7

3x - 4y = -2

2. You could solve the first equation for x by subtracting 2y from both sides:

x = 7 - 2y

3. Substitute the expression for the variable you solved for in step 1 into the other equation. For example, substituting x = 7 - 2y into the second equation gives:

3(7 - 2y) - 4y = -2

4. Simplify and solve for the remaining variable. Using the example from step 2, you would simplify the equation as follows:

21 - 6y - 4y = -2

21 - 10y = -2

-10y = -23

y = 23/10

5. Substitute the value of the variable you found in step 3 back into one of the original equations to solve for the other variable. Using the example from step 1, you would substitute y = 23/10 into x = 7 - 2y:

x = 7 - 2(23/10)

x = -9/5

6. Check your solution by substituting the values you found for x and y into both of the original equations. If the values satisfy both equations, then you have found the correct solution.

x + 2y = 7 becomes (-9/5) + 2(23/10) = 7, which is true

3x - 4y = -2 becomes 3(-9/5) - 4(23/10) = -2, which is also true

Therefore, the solution to the system of equations is x = -9/5 and y = 23/10.

User Joe Brunscheon
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