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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
Scelta multipla
Determine the number of solutions the system of equations has without graphing.
A
B
Infinitely Many
C
Guida verificata passo dopo passo1
Start with the given system of equations:
\[\begin{cases} y + 2x = 8 \\ y - 5x = -6 \end{cases}\]
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 and right sides:
\[ y + 2x - y + 5x = 8 + 6 \]
which reduces to
\[ 7x = 14 \]
Solve for x:
\[ x = \frac{14}{7} \]
Substitute the value of x back into one of the original equations (for example, the first one) to find y:
\[ y + 2\left(\frac{14}{7}\right) = 8 \]
Then solve for y to find the corresponding y-value.
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