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tatiyna
3 years ago
11

A line joins the point

Mathematics
1 answer:
Harrizon [31]3 years ago
5 0

Intersection of the first two lines:

\begin{cases}5x - 2y + 3 = 0\\4x - 3y + 1 = 0\end{cases}

Multiply the first equation by 4 and the second by 5:

\begin{cases}20x - 8y + 12 = 0\\20x - 15y + 5 = 0\end{cases}

Subtract the two equations:

(20x - 8y + 12)-(20x - 15y + 5)=0 \iff 7y+7=0 \iff y=-1

Plug this value for y in one of the equation, for example the first:

5x - 2\cdot (-1) + 3 = 0\iff 5x+5=0 \iff x=-1

So, the first point of intersection is (-1,-1)

We can find the intersection of the other two lines in the same way: we start with

\begin{cases}x=y\\x=3y+4\end{cases}

Use the fact that x and y are the same to rewrite the second equation as

x=3x+4 \iff 2x=-4 \iff x=-2

And since x and y are the same, the second point is (-2, -2)

So, we're looking for a line passing through (-1,-1) and (-2, -2). We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be y=x

In the attached figure, line 5x - 2y + 3 = 0 is light green, line 4x - 3y + 1 = 0 is dark green, and their intersection is point A.

Simiarly, line x=y is red, line x = 3y + 4 is orange, and their intersection is B.

As you can see, the line connecting A and B is the red line itself.

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3 years ago
A complete table with values for x or y that make this equation true:3x+y=15
Reika [66]

Answer:

Table is attached

Step-by-step explanation:

We are given equation as

3x+y=15

We will complete each column

First column:

we are given x=2 and we have to find y

3\times 2+y=15

6+y=15

y=9

Second column:

we are given y=3 and we have to find x

3x+3=15

3x=12

x=4

Third column:

we are given x=6 and we have to find y

3\times 6+y=15

18+y=12

y=-6

Fourth column:

we are given x=0 and we have to find y

3\times 0+y=15

0+y=15

y=15

Fifth column:

we are given x=3 and we have to find y

3\times 3+y=15

9+y=15

y=6

Sixth column:

we are given y=0 and we have to find x

3x+0=15

3x=15

x=5

Seventh column:

we are given y=8 and we have to find x

3x+8=15

3x=7

x=\frac{7}{3}

now, we can complete table



8 0
3 years ago
11. If Sally
Delvig [45]

Answer:

0.2

Step-by-step explanation:

Multiply 4/5 and 1/4: Decimal form

.8 • .25

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Why:

Take the 112.75 and multiply it by 1.2, or in other words 120%. You get 135.3, or in a money situation, $135.30. Good luck.

8 0
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