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spayn [35]
3 years ago
9

The graph of the equation x + 3y = 6 intersects at the y axis at the point whose coordinates are

Mathematics
1 answer:
svp [43]3 years ago
5 0

Answer:

4. (6,0)

Step-by-step explanation:

Plug the points into the equation.

6+3(0)=6

6+0=6

6=6

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A line joins the point
Harrizon [31]

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.

5 0
3 years ago
If i were to run from my house to my school, and it was 3 miles between, then how long would it take?
Triss [41]

Answer:

9 miles

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Plz help me, I'm not trying to fail math ​
spayn [35]
The answer is a i believe

you can solve it
8 0
3 years ago
Given a directed line segment with endpoints A(3, 2) and B(6, 11), what is the point that
bixtya [17]

The formula for a directed line is:

X = K1(X2) + (K2(X1) / K3

Y = K1(Y2) + (K2(Y1) / K3

K1 = numerator = 2

K2 = denominator - numerator = 3-2 = 1

K3 = denominator = 3

X = (2(6) + 1(3)) /3

X = (12+3) / 3

X = 12/3

X = 5

Y = (2(11) + 1(2)) /3

Y = (22 + 2) /3

Y = 24/3

Y = 8

The point is (5,8)

5 0
3 years ago
Read 2 more answers
Please help me asap!! Thank you
Setler79 [48]
-7z+42=-70
-7z= -112
z=16
4 0
3 years ago
Read 2 more answers
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