Question

question 1
when two graphs are parallel, what does this mean about their solutions?
○ the have no solution
○ not able to tell
○ they have an infinite amount of solutions

question 2
find the solution to the following system of equations:
y = -x + 2
y = 3x - 4
○ $\left(\frac{1}{2}, \frac{5}{2}\
ight)$
○ $\left(\frac{1}{2}, \frac{3}{2}\
ight)$
○ $\left(\frac{3}{2}, \frac{1}{2}\
ight)$
○ $\left(\frac{5}{2}, \frac{1}{2}\
ight)$

Explanation:

Question 1

For a system of linear equations represented by graphs, parallel lines have the same slope but different y - intercepts. This means the lines never intersect. The solution of a system of linear equations is the point of intersection of their graphs. If they never intersect, there is no solution.

Step1: Set the equations equal

Since both equations are solved for \(y\), we set \(-x + 2=3x - 4\).

Step2: Solve for \(x\)

Add \(x\) to both sides: \(2 = 4x-4\). Then add 4 to both sides: \(6 = 4x\). Divide both sides by 4: \(x=\frac{6}{4}=\frac{3}{2}\).

Step3: Find \(y\)

Substitute \(x = \frac{3}{2}\) into \(y=-x + 2\). So \(y=-\frac{3}{2}+2=-\frac{3}{2}+\frac{4}{2}=\frac{1}{2}\).

Answer:

A. The have no solution

Question 2