Question

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.

Answer 1

Answer:

  one point

Step-by-step explanation:

A system of two linear equations will have one point in the solution set if the slopes of the lines are different.

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When the equations are written in the same form, the ratio of x-coefficient to y-coefficient is related to the slope. It will be different if there is one solution.

• ratio for first equation: 1/1 = 1
• ratio for second equation: 1/-1 = -1

These lines have different slopes, so there is one solution to the system of equations.

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Additional comment

When the equations are in slope-intercept form with the y-coefficient equal to 1, the x-coefficient is the slope.

  y = mx +b . . . . . slope = m

When the equations are in standard form (as in this problem), the ratio of x- to y-coefficient is the opposite of the slope.

  ax +by = c . . . . . slope = -a/b

As long as the equations are in the same form, the slopes can be compared by comparing the ratios of coefficients.

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If the slopes are the same, the lines may be either parallel (empty solution set) or coincident (infinite solution set). When the equations are in the same form with reduced coefficients, the lines will be coincident if they are the same equation.