Question

How to Use Substitution to Solve a System of Two Linear Equations
1. Identify
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2. Isolate a
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3. Substitute that variable's
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into the other equation.
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the one-variable equation.
5. Substitute the value of that variable into the other
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6. Solve for the second
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7. Check your answer. Use
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Solve

Answer 1

To solve a system of two linear equations using substitution, follow these steps:

1. **Identify the method**: The substitution method is often the best choice when one equation is already solved for one variable or can be easily arranged to do so.
**Answer**: Substitution

2. **Isolate a variable**: Choose one equation and solve for one of the variables (usually \(x\) or \(y\)).
**Answer**: For example, if you have equations like \(y = 2x + 3\) and \(3x + 4y = 12\), you can isolate \(y\) in the first equation.

3. **Substitute that variable's expression**: Take the expression for the isolated variable and substitute it into the other equation.
**Answer**: Substitute \(y = 2x + 3\) into the second equation \(3x + 4(2x + 3) = 12\).

4. **Solve the one-variable equation**: Simplify and solve the resulting equation.
**Answer**: \(3x + 8x + 12 = 12\), then combine like terms to get \(11x + 12 = 12\), leading to \(11x = 0\), thus \(x = 0\).

5. **Substitute the value of that variable**: Now that you have a value for one variable, substitute it back into the equation you used to isolate the variable.
**Answer**: Substitute \(x = 0\) back into \(y = 2(0) + 3\) to find \(y\).

6. **Solve for the second variable**: This will give you the value of the second variable.
**Answer**: So, \(y = 3\).

7. **Check your answer**: Substitute both values into the original equations to ensure they hold true. Alternatively, you can graph both equations to see where they intersect.
**Answer**: Check by plugging \(x = 0\) and \(y = 3\) into both original equations to confirm they satisfy both, verifying your solution.

So, the solution to the system of equations is \( (x, y) = (0, 3) \).