객관식
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
Without using a graph, determine the number of solutions in the following systems of equations, then classify the system.
A
Independent and Consistent
B
Dependent and Consistent
C
Inconsistent
검증된 단계별 안내1
Step 1: Write down the system of equations clearly:
\[\begin{cases} y + 2x = 8 \\ y - 5x = -6 \end{cases}\]
Step 2: Use substitution or elimination to analyze the system. Here, both equations are solved for y, so set the right-hand sides equal to each other:
\[y + 2x = 8 \implies y = 8 - 2x\]
\[y - 5x = -6 \implies y = -6 + 5x\]
Set equal:
\[8 - 2x = -6 + 5x\]
Step 3: Solve the equation for x:
\[8 - 2x = -6 + 5x\]
Add 2x to both sides and add 6 to both sides:
\[8 + 6 = 5x + 2x\]
\[14 = 7x\]
Divide both sides by 7:
\[x = 2\]
Step 4: Substitute the value of x back into one of the original equations to find y:
Using \[y = 8 - 2x\]:
\[y = 8 - 2(2) = 8 - 4\]
\[y = 4\]
Step 5: Since there is exactly one solution (x=2, y=4), the system is consistent (has at least one solution) and independent (the equations represent two distinct lines).