Question

Варiант 2 1. Розв'яжіть графічно системи рівнянь 1) (2x – Зу = 6, 1 x-y= 0; 2. Скільки розв'язків має система рівнянь 1) x - 4y = 1, (2x – 8y = 3;Допоможіть, будь ласка, через 10 хв потрібно здати:)​

Answer 1

№2

х-4у=1                                                               2х-8у=3    

-4у=-х+1                                                            -8у=-2х+3

у=0,25х-1                                                           у=0,25х-0,75

дана система не має жодних розв'язків, тому що іх линейни функції у=kx+b має спильни  коєффіциент k, але різний b

Answer 2

System of Equations 1: (2x - 3y = 6, x - y = 0)

To solve the system of equations graphically, we can plot the equations on a coordinate plane and find the points of intersection. The points of intersection represent the solutions to the system of equations.

The first equation is 2x - 3y = 6, and the second equation is x - y = 0.

Let's solve this system of equations graphically:

1. Plot the first equation, 2x - 3y = 6: - To plot this equation, we need to find two points that satisfy the equation. - Let's choose x = 0 and solve for y: 2(0) - 3y = 6. Simplifying, we get -3y = 6, which gives us y = -2. - So, one point on the graph is (0, -2). - Now, let's choose y = 0 and solve for x: 2x - 3(0) = 6. Simplifying, we get 2x = 6, which gives us x = 3. - So, another point on the graph is (3, 0). - Plot these two points and draw a straight line passing through them.

2. Plot the second equation, x - y = 0: - To plot this equation, we again need to find two points that satisfy the equation. - Let's choose x = 0 and solve for y: 0 - y = 0. Simplifying, we get y = 0. - So, one point on the graph is (0, 0). - Now, let's choose y = 1 and solve for x: x - 1 = 0. Simplifying, we get x = 1. - So, another point on the graph is (1, 1). - Plot these two points and draw a straight line passing through them.

3. Find the point of intersection: - The point where the two lines intersect is the solution to the system of equations. - By visually inspecting the graph, we can see that the lines intersect at the point (2, 2).

Therefore, the system of equations 1) (2x - 3y = 6, x - y = 0) has one solution, which is x = 2 and y = 2.

[[1]]