Question

A system of equations is shown: 4x = −3y + 17 3x − 4y = −6 What is the solution to this system of equations? what lines are they, plz help

Answer 1

`\boxed{\sf \ \ \ x=2 \ \ y=3 \ \ \ }`

Explanation:

Hello, we have two equations and two unknowns

(1) 4x = -3y + 17

(2) 3x - 4y = -6

We can solve them algebraically

for instance from (1) we can divide by 4 and then write

(1')
`(4x)/(4)=x=(-3y+17)/(4)`

and then replace this expression of x in (2) it comes

`3*(-3y+17)/(4)-4y=-6 \ \ \ multiply \ by \ 4 \\<=> -3*3y+3*17-4*4y=-6*4\\<=> -9y+51-16y=-24 \ \ \ substract \ 51\\\\<=> -25y=-24-51=-75 \ \ \ divide \ by \ -25\\<=> y = (75)/(25)=3`

and then

`x=(-3*3+17)/(4)=(-9+17)/(4)=(8)/(4)=2`

we can solve it graphically as well

we just need to graph the two lines and find the intersection point as shown below

hope this helps