Question

Which point of intersection is the solution to the system of equations

Answer 1

Answer:

B

Step-by-step explanation:

(Looking at the lines in the graph, the second equation is missing a minus sign, and should be $y=-\frac{1}{3}x + \frac{2}{3}$)

To find the intersection point of the pair of linear equations, we just need to equate both values of y.

The equations are:

$y=\frac{2}{5}x - \frac{1}{2}$

$y=-\frac{1}{3}x + \frac{2}{3}$

Making the y from one equation equal the y of the other equation, we have:

$\frac{2}{5}x - \frac{1}{2} = -\frac{1}{3}x + \frac{2}{3}$

$\frac{2}{5}x +\frac{1}{3}x = \frac{2}{3} + \frac{1}{2}$

$\frac{6}{15}x +\frac{5}{15}x = \frac{4}{6} + \frac{3}{6}$

$\frac{11}{15}x = \frac{7}{6}$

$x = \frac{7}{6} * \frac{15}{11} =\frac{35}{22} = 1.591$

Then the y-coordinate of the point is found using this x-value in any of the two equations:

$y=\frac{2}{5}\frac{35}{22} - \frac{1}{2}$

$y=\frac{7}{11} - \frac{1}{2}$

$y=\frac{14}{22} - \frac{11}{22}$

$y=\frac{3}{22} = 0.136$

So the coordinate of the crossing point is (1.591, 0.136)

The point that is in this coordinate in the graph is point B.