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.
78
views
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
Start by writing the system of equations clearly:
\[\begin{cases} y + 2x = 8 \\ y - 5x = -6 \end{cases}\]
To determine the number of solutions without graphing, use the substitution or elimination method. Here, subtract the second equation from the first to eliminate \(y\):
\[ (y + 2x) - (y - 5x) = 8 - (-6) \]
Simplify the left side by canceling \(y\) and combining like terms:
\[ y + 2x - y + 5x = 8 + 6 \]
which simplifies to
\[ 7x = 14 \]
Solve for \(x\) by dividing both sides by 7:
\[ x = \frac{14}{7} \]
Substitute the value of \(x\) back into one of the original equations (for example, \(y + 2x = 8\)) to find \(y\):
\[ y + 2\left(\frac{14}{7}\right) = 8 \]
Then solve for \(y\).