Question

Question 3(Multiple Choice Worth 4 points)

(08.02)Which description best describes the solution to the following system of equations?

y = −x + 4
y = 3x + 3
Line y = −x + 4 intersects the line y = 3x + 3.
Lines y = −x + 4 and y = 3x + 3 intersect the x-axis.
Lines y = −x + 4 and y = 3x + 3 intersect the y-axis.
Line y = −x + 4 intersects the origin.

Answer 1

The correct option is (1).

Explanation:

The given system of equation is,

`y=-x+4` ..... (1)

`y=3x+3` .... (2)

The solution of the system of equation is the point where both line intersect each other.

Solve the equation by method of elimination.

Multiply equation 1 by 3.

`3y=-3x+12` ... (3)

Add equation (2) and (3).

`y+3y=3x+3+(-3x+12)`

`4y=3x+3-3x+12`

`4y=15`

`y=3.75`

Put this value in equation 1.

`3.75=-x+4`

`x=-3.75+4`

`x=0.25`

Therefore, the lines intersect each other at (0.25,3.75). So, the first option is correct.