Which graph represents the solution of the system StartLayout Enlarged left-brace 1st row x squared + y squared = 4 2nd row x minus y = 1 EndLayout?
On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 4 units. The line has a negative slope and goes through (negative 3, 4), (0, 1), and (1, 0).
On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 2 units. The line has a positive slope and goes through (negative 3, negative 4), (0, negative 1), and (1, 0).
On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 4 units. The line has a positive slope and goes through (negative 3, negative 4), (0, negative 1), and (1, 0).
On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 2 units. The line has a negative slope and goes through (negative 3, 4), (0, 1), and (1, 0).

This is nonlinear system of equations, notice that it's about the intersection between a circle and a line, which can be in one point (tangent) or in two points (secant).

Let's isolate [tex]x[/tex] in the second equation, and then we replace that expression into the first equation

[tex]x=y+1[/tex]

[tex]x^{2} +y^{2} \\(y+1)^{2} +y^{2} =4\\y^{2}+ 2y+1+y^{2}=4 \\2y^{2} +2y-3=0[/tex]

Using a calculator, the solutions are

[tex]y_{1} \approx 0.8\\y_{2} \approx -1.8[/tex]

Now, we use these values, to find their pairs.

[tex]x=y+1\\x=0.8+1 \approx 1.8[/tex]

[tex]x=y+1\\x=-1.8+1 \approx -0.8[/tex]

Therefore, the solutions of the system are [tex](1.8,0.8)[/tex] and [tex](-0.8, -1.8)[/tex].

The image attached shows the solutions graphically.

ryantraylor36 ryantraylor36 · Answer 2 · 2022-06-14T09:50:11+02:00

ryantraylor36 ryantraylor36

14-06-2022

Answer:

B

Step-by-step explanation:

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