Question

How do I solve this doing "solving liner systems by combination"

Answer 1

To solve a system of linear equations by combination, use the method of elimination to eliminate one variable by adding or subtracting the equations together.

Step-by-step explanation:

To solve a system of linear equations by combination, you use the method of elimination to eliminate one of the variables by adding or subtracting the equations together. Here are the steps:

1. Write down the equations in the system.
2. Choose a variable to eliminate by multiplying one or both equations by a constant.
3. Add or subtract the equations to eliminate the chosen variable.
4. Solve the resulting equation to find the value of the remaining variable.
5. Substitute the value of the remaining variable back into one of the original equations to solve for the other variable.
6. Check your solution by substituting the values into both original equations.

Answer 2

Remember that the steps to solve a system of linear equations (2x2) are:

0. Arrange the equations with like terms in columns.

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1. Analyze the coefficients of x or y, and try to eliminate one.

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2. Add the equations and solve for the remaining variable.

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3. Substitute the value into either equation and solve.

Notice that if we multiply equation 1 by -2 and add it up with equation 2, we'll eliminate x , as following:

`\begin{gathered} \begin{cases}2x-y=2 \\ 4x+3y=24\end{cases}\rightarrow\begin{cases}-4x+2y=-4 \\ 4x+3y=24\end{cases} \\ \\ \rightarrow5y=20\rightarrow y=(20)/(5)\Rightarrow y=4 \end{gathered}`

Now, we plug in this value in equation 2 and solve for x :

`\begin{gathered} 4x+3y=24\rightarrow4x+3(4)=24\rightarrow4x+12=24 \\ \rightarrow4x=12\rightarrow x=(12)/(4)\Rightarrow x=3 \end{gathered}`