Math  /  Algebra

QuestionSolve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system. {2x+y=44x+2y=3\left\{\begin{array}{l} 2 x+y=4 \\ 4 x+2 y=3 \end{array}\right.
Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. The solution is x=x= \square and y=y= \square . (Type integers or simplified fractions.) B. There are infinitely many solutions. Using ordered pairs, they can be expressed as {(x,y)x=\{(x, y) \mid x= \square , y is any real number }.\}. (Simplify your answer. Type an expression using y as the variable as needed.) C. The system is inconsistent.

Studdy Solution
To graph the lines, rewrite each equation in slope-intercept form (y=mx+b y = mx + b ):
Equation 1: y=2x+4 y = -2x + 4
Equation 2: y=2x+32 y = -2x + \frac{3}{2}
Graph these lines on the same coordinate plane. Notice that they are parallel lines with different intercepts, confirming that there is no intersection point and thus no solution.

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