Question

Answer two questions about Systems A and B:
A: x−4y=1
5x+6y=−5
B: x=1+4y
5x+6y=−5
How can we get System B from System A?
​A: Replace one equation with itself where a quantity is added to only one side
B: Replace one equation with itself where the same quantity is added to both sides
C: Swap only the right-hand sides of both equations
D: Swap the order of the equations

Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
A: Yes
B: No

Answer 1

Answer:

Replace one equation with itself where the same quantity is added to both sides

Yes

Answer 2

Yes, the systems are equivalent. In other words, they have the same solution.

What is a linear equation?

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The Systems of equation given for A and B:

A: x−4y=1

5x+6y=−5

B: x=1+4y

5x+6y=−5

So, we get System B from System A by the following step;

A; Replace one equation with itself where the same quantity is added to both sides.

Hence, Yes the systems are equivalent. In other words, they have the same solution.

Learn more about linear equations;

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