Where do the lines y=2x+1 and y=-5x-6 intersect?

Mathematics

2 answers:

Gnoma [55]3 years ago

5 0

Answer:

(-1, -1)

Step-by-step explanation:

To find where two lines in slope-intercept form intersect, set them equal to each other.

2x + 1 = -5x - 6

7x = -7

x = -1

Knowing they intersect at x = -1, substitute -1 into either of the two equations to find the y-value of their intersection.

y = 2(-1) + 1

y = -2 + 1

y = -1

So the intersection point of the two lines is (-1, -1).

kipiarov [429]3 years ago

3 0

Answer: (-1,-1)

Explanation:

I added a picture

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Which equation does the graph of the systems of equations solve?

mihalych1998 [28]

Answer:

$\text{B. }\frac{1}{3}x-3=-x+1$

Step-by-step explanation:

Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to $(x_1,y_1)$ and $(x_2, y_2)$ (doesn't matter which you assign) and use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let:

$(x_1,y_1)\implies (0,1)\\(x_2,y_2)\implies (1, 0)$

The slope is equal to:

$m=\frac{0-1}{1-0}=\frac{-1}{1}=-1$

Therefore, the slope of this line is -1. In slope-intercept form $y=mx+b$ , $m$ represents slope, so one of the lines must have a term with $-x$ in it, which eliminates answer choices A and D.

For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:

$(x_1,y_1)\implies (0,-3)\\(x_2,y_2)\implies (3, -2)$

Using the slope formula:

$m=\frac{-2-(-3)}{3-0}=\frac{1}{3}$

Thus, the slope of the line is 1/3 and the other line must have a term with $\frac{1}{3}x$ in it, eliminating answer choice C and leaving the answer $\boxed{\text{B. }\frac{1}{3}x-3=-x+1}$