Question

Understand Systems of Linear Equations - Ouiz - Level H

y=-2x+4
y = 2x

* How many solutions does the system of equations have?

* One solution

What is the solution to the system of equations?

(2, 2)

(1, 1)

(1, 2)

(2,1)

Answer 1

There is only one solution and the solution is (0,4).

Explanation:

The given system has equations;

and

We equate the two equations to determine their point of intersection;

We put x=0 into the first equation to get;

There is only one solution and the solution is (0,4).

Answer 2

Because we’re looking for the intersection point of the two linear equations, we know that x and y will be equal. If the two lines cross at a point, they will share the same x and y-coordinates. Therefore, we can set both equations equal to each other since we are looking for the same point (x, y) in both equations and because both equal y.

(2x)=-2x+4

Solve for x:

Add 2x to both sides:

2x+2x=4

4x=4

Divide both sides by 4:

4x/4=4/4

x=1

Now, to find y, plug x=1 into one of the original equations:

y=2(1)

y=2

Thus, the answer is One Solution and (1, 2)