To find the ordered pair that is a solution to the system of equations given by \(y = 3x + 2\) and \(y = -2x + 12\), we can start by calculating the values of \(y\) for the provided \(x\) values in each equation.
Let's take the given values: \(x = -2, -1, 0, 1, 2\).
For the equation \(y = 3x + 2\):
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When \(x = -2\):
\(y = 3(-2) + 2 = -6 + 2 = -4\) -
When \(x = -1\):
\(y = 3(-1) + 2 = -3 + 2 = -1\) -
When \(x = 0\):
\(y = 3(0) + 2 = 0 + 2 = 2\) -
When \(x = 1\):
\(y = 3(1) + 2 = 3 + 2 = 5\) -
When \(x = 2\):
\(y = 3(2) + 2 = 6 + 2 = 8\)
For the equation \(y = -2x + 12\):
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When \(x = -2\):
\(y = -2(-2) + 12 = 4 + 12 = 16\) -
When \(x = -1\):
\(y = -2(-1) + 12 = 2 + 12 = 14\) -
When \(x = 0\):
\(y = -2(0) + 12 = 0 + 12 = 12\) -
When \(x = 1\):
\(y = -2(1) + 12 = -2 + 12 = 10\) -
When \(x = 2\):
\(y = -2(2) + 12 = -4 + 12 = 8\)
Summary of results:
| x | \(y = 3x + 2\) | \(y = -2x + 12\) | |----|-----------------|-------------------| | -2 | -4 | 16 | | -1 | -1 | 14 | | 0 | 2 | 12 | | 1 | 5 | 10 | | 2 | 8 | 8 |
Identify the intersection:
Looking at the results, we can see that for \(x = 2\), both equations yield \(y = 8\). Therefore, the ordered pair \((2, 8)\) is a solution to the system of equations.
The ordered pair that is a solution to the system of equations is \((2, 8)\).