xy-4x+20 y2= 5x-7

0

20

-7

1

16

-2

2

12

3

3

8

8

4

4

13

5

0

18

What is the solution to the system of equations (y1 = -4x + 20 ? (y2 = 5x - 7

A. (3,8)

В. (3,13)

c. (4,13)

D. (20-7)

1 answer

To find the solution to the system of equations given by \(y_1 = -4x + 20\) and \(y_2 = 5x - 7\), we need to set the two equations equal to each other since at the point of intersection \(y_1\) and \(y_2\) will have the same value.

  1. Set the equations equal: \[ -4x + 20 = 5x - 7 \]

  2. Solve for \(x\): \[ 20 + 7 = 5x + 4x \ 27 = 9x \ x = 3 \]

  3. Now that we have \(x\), substitute it back into either equation to find \(y\). We'll use \(y_1\): \[ y = -4(3) + 20 \ y = -12 + 20 \ y = 8 \]

Thus, the solution to the system of equations is \((3, 8)\).

So the answer is A. (3, 8).