Pregunta
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Solve the following system of equations graphically on the set of axes below.

Ask by Huang Chandler. in the United States
Dec 20,2024

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The solution is .

Solución

Solve the system of equations .
Solve the system of equations by following steps:
  • step0: Solve using the substitution method:
  • step1: Substitute the value of
  • step2: Simplify:
  • step3: Move the constant to the right side:
  • step4: Subtract the numbers:
  • step5: Divide both sides:
  • step6: Divide the numbers:
  • step7: Substitute the value of
  • step8: Simplify:
  • step9: Calculate:
  • step10: Check the solution:
  • step11: Rewrite:

    The solution to the system of equations is .

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Beyond the Answer

To solve the system of equations graphically, you can start by rewriting both equations in slope-intercept form , where is the slope and is the y-intercept.
  1. The first equation is already in slope-intercept form:
    Here, the slope is and the y-intercept is . You can plot this line by starting at the y-intercept (0, 3) and using the slope to find the next points. From (0, 3), you can move up 1 unit and 3 units to the right to get to (3, 4) and then down 1 unit and 3 units to the left to get to (-3, 2).
  2. Now, rearranging the second equation to slope-intercept form involves isolating :
    Here, the slope is and the y-intercept is . Starting at the point (0, -3), you can move down 5 units and right 3 units to plot another point at (3, -6) and similarly up 5 units and left 3 units for more.
  3. Now you plot both lines on the same set of axes. The lines will intersect at some point; that intersection point represents the solution to the system of equations.
By plotting both lines accurately and finding their intersection, you can determine the solution graphically. Once you have done this, you can read off the coordinates of the intersection point, which gives you the values of and that satisfy both equations.

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