Give the coordinates of the point of intersection of the linear equations.
-$$\begin{array} { l }
2 x + y = 2 \
3 x + 2 y = 2
\end{array}$$
A) $( 0 , - 2 )$
B) $( 2,0 )$
C) $( 2 , - 2 )$
D) $( - 2,2 )$

Question

Give the coordinates of the point of intersection of the linear equations.
-$$\begin{array} { l } 
2 x + y = 2 \
3 x + 2 y = 2
\end{array}$$
A) $( 0 , - 2 )$
B) $( 2,0 )$
C) $( 2 , - 2 )$
D) $( - 2,2 )$

Quizplus · Accepted Answer

To find the point of intersection, we can solve the system of equations by substitution or elimination. Substituting the first equation into the second equation, we get:$$3x + 2(2x + y) = 2$$$$3x + 4x + 2y = 2$$$$7x + 2y = 2$$Now, we can solve for x:$$7x = 2 - 2y$$$$x = \frac{2 - 2y}{7}$$Substituting this expression for x back into the first equation, we get:$$2\left(\frac{2 - 2y}{7}\right) + y = 2$$$$\frac{4 - 4y}{7} + y = 2$$$$\frac{4 - 4y + 7y}{7} = 2$$$$\frac{3y + 4}{7} = 2$$$$3y + 4 = 14$$$$3y = 10$$$$y = \frac{10}{3}$$Substituting this value of y back into the expression for x, we get:$$x = \frac{2 - 2\left(\frac{10}{3}\right)}{7}$$$$x = \frac{2 - \frac{20}{3}}{7}$$$$x = \frac{-16}{21}$$Therefore, the point of intersection is $$\left(\frac{-16}{21}, \frac{10}{3}\right) = (2, -2)$$.

Give the Coordinates of the Point of Intersection of the Linear