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Algebra / Systems of two linear equations in two variables Difficulty: Hard

$Equation 1: y equals, one half x, plus 8. Equation 2: y equals, c x plus 10.$

In the system of equations above, c is a constant. If the system has no solution, what is the value of c ?

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Explanation

The correct answer is $one half$ . A system of two linear equations has no solution when the graphs of the equations have the same slope and different y-intercepts. Each of the given linear equations is written in the slope-intercept form, $y equals, m x plus b$ , where m is the slope and b is the y-coordinate of the y-intercept of the graph of the equation. For these two linear equations, the y-intercepts are $the points with coordinates 0 comma 8$ and $0 comma 10$ . Thus, if the system of equations has no solution, the slopes of the graphs of the two linear equations must be the same. The slope of the graph of the first linear equation is $one half$ . Therefore, for the system of equations to have no solution, the value of c must be $one half$ . Note that 1/2 and .5 are examples of ways to enter a correct answer.