Multiple Choice
Use the graph to identify the solution to the system of equations or identify that the system has or infinitely many solutions. If there is a solution, check that the point satisfies both equations.
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5. Systems of Linear Equations
Solving Systems of Linear Equations by Graphing
Multiple Choice
Determine the number of solutions the system of equations has without graphing.
A
B
Infinitely Many
C
Verified step by step guidance1
Identify the slopes of both equations. The slope is the coefficient of \(x\) in each equation. Here, both slopes are \(\frac{1}{4}\).
Compare the slopes. Since both slopes are equal, the lines are either parallel or the same line.
Check the y-intercepts (the constant terms). The first equation has a y-intercept of \$11\(, and the second has a y-intercept of \)-6$.
Since the slopes are equal but the y-intercepts are different, the lines are parallel and will never intersect.
Conclude that the system has no solutions because parallel lines do not intersect.