Question

Consider the following system of equations:

y = −x + 2
y = 3x + 1

Which description best describes the solution to the system of equations?

a
Line y = −x + 2 intersects line y = 3x + 1.

b
Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.

c
Lines y = −x + 2 and y = 3x + 1 intersect the y-axis.

d
Line y = −x + 2 intersects the origin.

Answer 1

Step-by-step explanation:To solve the system of equations, we can set the two expressions for y equal to each other:

−x + 2 = 3x + 1

Solving for x, we get:

4x = 1

x = 1/4

Substituting this value of x into either of the original equations, we get:

y = −(1/4) + 2

y = 7/4

Therefore, the solution to the system of equations is the point (1/4, 7/4), which is the point of intersection of the two lines.

So the correct description of the solution to the system of equations is:

a

Line y = −x + 2 intersects line y = 3x + 1.