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Question

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What is the solution to the system of equations y = 3x +2
and y =−2x+12
?

Complete the table to support your answer.

(1 point)
x values y = 3x +2
y =−2x+12
-2
-1
0
1
2
The ordered pair that is a solution to the system of equations is
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Answer 1

To find the solution to the system of equations given by \(y = 3x + 2\) and \(y = -2x + 12\), we can set the two equations equal to each other to find the point where they intersect.

1. Set the two equations equal: \[ 3x + 2 = -2x + 12 \]

2. Solve for \(x\): \[ 3x + 2x = 12 - 2 \ 5x = 10 \ x = 2 \]

3. Now substitute \(x = 2\) back into either equation to find the corresponding \(y\) value. We'll use \(y = 3x + 2\): \[ y = 3(2) + 2 = 6 + 2 = 8 \]

Thus, the solution to the system of equations is the ordered pair \((2, 8)\).

Next, let's complete the table by calculating the values of \(y\) for each \(x\) according to both equations.

| x values | \(y = 3x + 2\) | \(y = -2x + 12\) | |----------|----------------|-------------------| | -2 | \(3(-2) + 2 = -6 + 2 = -4\) | \(-2(-2) + 12 = 4 + 12 = 16\) | | -1 | \(3(-1) + 2 = -3 + 2 = -1\) | \(-2(-1) + 12 = 2 + 12 = 14\) | | 0 | \(3(0) + 2 = 0 + 2 = 2\) | \(-2(0) + 12 = 0 + 12 = 12\) | | 1 | \(3(1) + 2 = 3 + 2 = 5\) | \(-2(1) + 12 = -2 + 12 = 10\) | | 2 | \(3(2) + 2 = 6 + 2 = 8\) | \(-2(2) + 12 = -4 + 12 = 8\) |

From the calculations shown in the table, we verify that for \(x = 2\), the output of both equations is \(y = 8\), confirming that the solution to the system of equations is indeed the ordered pair \((2, 8)\).