Answer:
(x,y)=(6,-2)
Step-by-step explanation:
to understand this
you need to know about:
- linear equation
- system of linear equation
- solving system of linear equation by graphing
- PEMDAS
given:
- [tex] \begin{cases} \sf x + y = 4 \\ \sf7x - 6y = 54 \end{cases}[/tex]
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
[tex] \sf7x - 6y = 54[/tex]
[tex] \sf - 6y = - 7x + 54 \\ \sf \frac{ - 6y}{ - 6} = \frac{ - 7}{ - 6} x + \frac{54}{ - 6} \\ \sf y = \frac{7}{6} x - 9[/tex]
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
