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How Do You Graph a System of Equations With No Solution?

Find the solution(s) to the following system of equations: 2x – y = 2 and 4x – 2y = 8

Summary

  1. 'x' and 'y' are the variables in the given system of two equations
  2. To find the solution, we need to find the values of 'x' and 'y' that make both equations true
  3. Converting the given equations to slope-intercept form will help us graph the equations
  4. (A) stands for y=2x-2
  5. (B) stands for y=2x-4
  6. When we graph (A) and (B), we get two parallel lines!
  7. The solution to the given solution is the intersection of (A) and (B). Since parallel lines never cross, there is no solution!
  8. A system of equations with no solution is 'inconsistent'.

Notes

    1. Converting the given equations to slope-intercept form will help us graph the equations
    2. Slope-intercept form looks like y=mx+b, where m is the slope of the line, and b is the y-intercept of the line
    3. 'x' and 'y' are the variables in the given system of two equations
    1. We need to take 2x-y=2, and convert it to slope-intercept form
    2. (1): Use the subtraction property of equality to subtract 2x from both sides and isolate -y
    3. (2): Use the multiplication property of -1 and multiply both sides by -1 to convert -y to y
    4. If you'd like to see this done in more detail, check out the last link below!
    1. We need to take 4x-2y=8, and convert it to slope-intercept form
    2. (1): Use the subtraction property of equality to subtract 4x from both sides and isolate -2y
    3. (2): Use the multiplication property of -1 and multiply both sides by -1 to convert -2y to 2y. Then divide both sides by 2 to isolate y!
    1. The given equations are lines in the coordinate plane, and the solution to the given system is where the lines cross!
    2. The coordinate plane is the space that consists of the x and y-coordinate axes.
    3. The lines are in slope-intercept form, which lets you see the slope and intercept of each line without much trouble!
    1. The slope is positive 2, and that means that going up 2 units and over 1 unit will take us from one point to another
    1. Remember, the intersection of the graphed lines will give you the solution to the given system!
    2. Notice that the graphed lines are parallel though!
    3. Just looking at the slope-intercept form of the line tells you that these lines are parallel. See the last link below for more about that!