Question

At what point do the two linear equations intersect? y=2-x y=2x+5

Answer 1

(-1, 3)

Explanation:

We can find the intersection point by solving the system of equations! First, find the value of X.

y = 2 - x

y = 2x + 5

To find the value of X, simply combine both equations because both equations are equal to Y.

2 - x = 2x + 5

Then, solve for X by moving terms!

2 - 3x = 5

-3x = 3

-x = 1

x = -1

Now, substitute x = -1 into y = 2x + 5!

y = -2 + 5

y = 3

There you have it, x = -1 and y = 3 are your points. The answer is (-1. 3)!

Answer 2

(-1, 3)

Explanation:

A point of intersection is a point where two or more lines or curves meet. It is the only point that is common to all of the lines or curves.

In this case:

In order to find the point of intersection of the two linear equations, we can set them equal to each other and solve for x and y.

y=2-x

y=2x+5

Setting the two equations equal to each other, we get:

`\sf 2-x = 2x+5`

Adding x and subtracting 5 on both sides:

`\sf 2 -x+x-5 =2x+5+x-5`

Combining like terms, we get:

3x = -3

Dividing both sides by -3, we get:

`\sf (3x)/(3)=-(3)/(3)`

`\sf x = -1`

Substituting this value of x into the first equation, we get:

`\sf y=2-(-1)`

`\sf y=3`

Therefore, the two linear equations intersect at the point (-1, 3).