Question

Solve the system of equations by graphing. [x+y=4 7x-6y=54​

Answer 1

(x,y)=(6,-2)

Explanation:

to understand this

you need to know about:

• linear equation
• system of linear equation
• solving system of linear equation by graphing
• PEMDAS

given:

• 
  `\begin{cases} \sf x + y = 4 \\ \sf7x - 6y = 54 \end{cases}`

tips and formulas:

• to solve system of linear equation by graphing we have to simplify the linear equations to slope-intercept form
• slope intercept form:y=mx+b

let's solve:

let's simplify first linear equation to slope -intercept form

x+y=4

y=-x+4

table for this equation

see the first attachment picture

let's simplify first linear equation to slope -intercept form

`\sf7x - 6y = 54`

`\sf - 6y = - 7x + 54 \\ \sf ( - 6y)/( - 6) = ( - 7)/( - 6) x + (54)/( - 6) \\ \sf y = (7)/(6) x - 9`

table for this equation

see the second attached picture

solutions by graphing the system of linear equation

see the last attached picture

note: the red line is for first equation as well as the green line is for second equation and the black dot is the coordinates of the solutions of x and y