Studdy AI Logo
Math

QuestionFind where the lines y=−xy = -x and y=25x−7y = \frac{2}{5}x - 7 intersect.

Studdy Solution

STEP 1

Assumptions1. The two given equations are linear equations. . The point of intersection is the point where both equations are equal to each other.

STEP 2

To find the point of intersection, we need to set the two equations equal to each other and solve for x.
−x=25x−7-x = \frac{2}{5}x -7

STEP 3

We can solve for x by adding x to both sides of the equation to get all the x terms on one side.
−x+x=25x−7+x-x + x = \frac{2}{5}x -7 + x

STEP 4

implify the equation.
0=7x−70 = \frac{7}{}x -7

STEP 5

Next, add7 to both sides of the equation to isolate the x term.
0+7=75x−7+70 +7 = \frac{7}{5}x -7 +7

STEP 6

implify the equation.
=5x = \frac{}{5}x

STEP 7

To solve for x, we divide both sides of the equation by 75\frac{7}{5}.
x=775x = \frac{7}{\frac{7}{5}}

STEP 8

implify the equation to find the x-coordinate of the point of intersection.
x=5x =5

STEP 9

Now that we have the x-coordinate, we can find the y-coordinate by substituting x =5 into one of the original equations. Let's use the first equation y=−xy = -x.
y=−5y = -5So, the point of intersection for the two linear equations y=−xy = -x and y=25x−7y = \frac{2}{5}x -7 is (5,−5)(5, -5).

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord