Lisa id working with yhe system of equations x+2y=7 and 2x-5y=5. She multiplies the forst equation by 2 and then subtracts the second equation to find 9x=9, telling her y=1. Lisa then figures out the x=5. Thinking about the procedure, lisa wonders: there are lots of ways I could solve the problem. I could add 5 times the first equation and twice the second or I could multiply the first equation by -2 and add the second. I seem to find that there are only one solution to the two equations, but I wonder if I will get the same solution if I use a different method? A. What is the answer to Lisa's question? Explain. B. Does the answer to (a) change if we have a system of two equations in two unknowns with no solution? What if there are infinitely many solutions?
Answers
Answer:
Step-by-step explanation:
Answer (A):
Whatever above mentioned methods she applies, the answer will come out to be y=1 and x=5. These values satisfies both the equations.
Answer (B):
The answer won't change for the system with two unknowns with no solution because these points (x,y)=(5,1) represents the same point of intersection when plotted on graph.Moreover, this point gives unique solution.
Answer (C):
If there are infinitely many solutions then it means that the system is dependent.It means that when we plot them on a graph, all points are common between them and they happen to come on one line.
Answer:
Step-by-step explanation:
−
2
x
+
y
=
1
, isolate
y
by adding
−
2
x
to both sides of the equation. This will give you
y
=
1
+
2
x
.
Substitute
1
+
2
x
for
y
into the other equation.
Solve for x:
−
4
x
+
2
(
1
+
2
x
)
=
−
8
−
4
x
+
2
+
4
x
=
−
8
2
≠
−
8