Question

Worth 60 points

Answer 1

Answer:

Line y = -x + 2 intersects line y = 3x + 1

Step-by-step explanation:

The solution to a system of equations is the point at which the two lines intersect.  To find this point, first equate the equations and solve for x:

$\begin{aligned}y & = y\\-x + 2 & = 3x + 1\\-x+2+x & = 3x+1+x\\2 & = 4x + 1\\2-1 & =4x+1-1\\1 &=4x\\x & =\dfrac14\end{aligned}$

Substitute the found value of x into one of the equations, and solve for y:

$y=3\left(\dfrac14\right)+1=\dfrac74$

Therefore, the solution to the system of equations (the point at which the two lines intersect) is:

$\left(\dfrac14,\dfrac74\right)$

So the description that best describes the solution to the system of equations is:

Line y = -x + 2 intersects line y = 3x + 1