Question

Please help: “Solve the system of two equations and enter the value of only y- coordinate:

2x-3y = 12, 2x -7y = 4
y-coordinate is”

some help would be really appreciated, thanks

Answer 1

The y-coordinate of the given system of equations is y = 2.

Explanation:

Given system of equations:

`\begin{cases}2x-3y = 12\\ 2x -7y = 4\end{cases}`

Subtract the second equation from the first equation to eliminate the terms in x :

`\begin{array}{crcccl}&2x&-&3y&=&12\\\vphantom{\frac12}-&(2x&-&7y&=&\:\:4)\\\cline{2-6}\vphantom{\frac12}&&&4y&=&\:\:8\\\cline{2-6}\end{array}`

Solve the equation for y by dividing both sides of the equation by 4:

`\implies 4y=8`

`\implies (4y)/(4)=(8)/(4)`

`\implies y=2`

Therefore, the y-coordinate of the given system of equations is:

• y = 2

The solution to a graphed system of equations is the point of intersection of the two lines. Therefore, to confirm the y-coordinate of the given system of equations is y = 2, graph the two lines and check the y-coordinate of the point of intersection. (See attachment).