Question

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

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

Answer 1

y = -x + 4
y = 3x + 3

3x + 3 = -x + 4
3x + x = 4 - 3
4x = 1
x = 1/4

y = 3x + 3
y = 3(1/4) + 3
y = 3/4 + 3
y = 3/4 + 12/4
y = 15/4

solution is (1/4,15/4)

so line y = -x + 4 intersects the line y = 3x + 3 at (1/4,15/4)