Question

Question 10 of 10

Using the graphing function on your calculator, find the solution to the system
of equations shown below.
2y-4x=6
y-2x=7
OA. More than 1 solution
B. x = 4, y = -2
C. x = -1, y = 1
D. No solution

Answer 1

First isolate y on both then graph

• 2y-4x=6
• 2y=4x+6
• y=2x+3--(1)

And

• y-2x=7
• y=2x+7

Update:-

In both equations slope is equal so lines are parallel hence no solutions

Answer 2

D. no solution

Explanation:

Given system of equations:

`\begin{cases}2y-4x=6\\y-2x=7\end{cases}`

The solution to a graphed system of equations is the point(s) of intersection.

From inspection of the graphs (attached), there is no point of intersection so there is no solution.

Proof

Rearrange the given equations to make y the subject:

Equation 1

`\implies 2y-4x=6`

`\implies 2y=4x+6`

`\implies y=2x+3`

Equation 2

`\implies y-2x=7`

`\implies y=2x+7`

Slope-intercept form of a linear equation:
`y=mx+b`

(where m is the slope and b is the y-intercept)

Therefore, the slope of both equations is 2. When the slopes of two lines are the same, the lines are parallel ("inconsistent") and therefore never intersect. Hence proving that there is no solution to the given system of equations.