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10:01 PM Sun Mar 9 \( 12 \% \) © hmhco.com STECY GUERRIER 11 of 11 DIRECTIONS: Use this information to answer Parts A and B. Spiral Review Solve the system of equations by graphing. \[ \begin{array}{l} y=4-3 x \\ y=2-x \end{array} \] Part A Use the Line Tool to graph the system of equations. Show Hints Line Undo Redo \( \times \) Reset

Ask by Floyd Hampton. in the United States
Mar 10,2025

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Answer

The solution to the system is \( (1, 1) \).

Solution

1. Set the equations equal to each other to find \( x \): \[ 4 - 3x = 2 - x \] 2. Subtract \( 2 \) from both sides: \[ 2 - 3x = -x \] 3. Add \( 3x \) to both sides: \[ 2 = 2x \] 4. Divide both sides by \( 2 \): \[ x = 1 \] 5. Substitute \( x = 1 \) into one of the original equations (for example, \( y = 2 - x \)): \[ y = 2 - 1 = 1 \] The solution to the system is: \[ (x, y) = (1, 1) \]

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Bonus Knowledge

To solve the system of equations by graphing, you would first graph each equation on the same coordinate plane. For the first equation \( y = 4 - 3x \), start by plotting the y-intercept at (0, 4) and then find another point using the slope of -3 (for every 1 unit you move right, move down 3 units). For the second equation \( y = 2 - x \), plot the y-intercept at (0, 2) and use the slope of -1 to find an additional point. Once both lines are graphed, their intersection point will give you the solution to the system of equations. When graphing, keep an eye out for common mistakes! One frequent error is miscalculating the slope or missing the y-intercept. Always double-check that the slope used correctly represents the rise over run, and make sure you mark the points accurately. If the lines don't intersect, that indicates the system has no solution—an important detail to recognize!

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