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Kamila [148]
3 years ago
9

The first line in the system of equations is graphed on the coordinate plane. Graph the second line to find the solution to the

Mathematics
1 answer:
fiasKO [112]3 years ago
8 0

Answer:

See attachment.

Step-by-step explanation:

The given system is   2x-3y=-6\\y=-x-4

The first line is already graphed.

We want to graph y=-x-4

We can do this by plotting two points and drawing a straight line through them.

When we choose x=0, we substitute into the equation and solve for y.

y=-0-4=-4

So we plot (0,-4)

Also, when y=0, we substitute and solve for x.

0=-x-4\implies x=-4

So we plot the point (-4,0)

We now use a straight edge to draw a straight line through these two points to obtain the graph shown in the attachment.

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<u>Step-by-step explanation:</u>

Use the Double Angle Identity:  cos 2A = 2cos²A - 1

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<u>Proof  LHS → RHS</u>

\text{Given:}\qquad \qquad \qquad \qquad 2\cos^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)-1\\\\\\\text{Double Angle Identity:}\quad \cos2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \quad \cos\bigg(\dfrac{\pi}{2}-A\bigg)\\\\\\\text{Difference Identity:}\qquad \cos\dfrac{\pi}{2}\cdot \cos A+\sin \dfrac{\pi}{2}\cdot \sin A\\\\\\\text{Unit Circle:}\qquad \qquad \qquad 0\cdot \cos A+1\cdot \sin A\\\\\\\text{Simplify:}\qquad \qquad \qquad \qquad \sin A

LHS = RHS:   sin A = sin A   \checkmark

 

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