Question

What is the solution to the system of equations graphed below?
y=-4x+ 33
y=5/3x-1

Answer 1

Answer:

x = 6, y = 9 is the solution to the given system of equations.

Step-by-step explanation:

Here, the system of the equations is:

$y = -4x + 33\\y = \frac{5}{3}x -1$

Now, substitute the value of y in the second equation, we get

$-4x + 33 = \frac{5}{3} x - 1$

⇒$33 + 1 = \frac{5x}{3}  + 4x$

or, [tex]\frac{5x + 12x}{3}  = 34[/tex}

or, 17x = 3 x 34 = 102

So, x = 102 / 17 = 6

⇒x = 6  :  putting this in (1),

y = -4x + 33 = - 24 + 33 = 9

Hence, x = 6, y = 9 is the solution to the given system of equations.

Answer 2

Answer:

$x=6\\y=9$

Step-by-step explanation:

The system we have:

$y=-4x+ 33\\y=\frac{5}{3} x-1$

we can solve the system by eliminating one of the variables, I will eliminate the 'y' variable by substracting the equations:

$y=-4x+ 33\\-(y=\frac{5}{3} x-1)\\---------------\\y=-4x+ 33\\-y=-\frac{5}{3} x+1\\\\-----------------\\0y=-4x-\frac{5}{3} x+33+1$

we have $0y$ which is zero, so now we have an equation that only depends on 'x'.

so now solving the resulting equation for 'x'

$0=-\frac{17}{3} x+34\\-34=-\frac{17}{3} x\\\frac{(34)(3)}{17}=x\\ 6=x$

we have the value for x. Now we substitute this in the first of the original equations of the system to find the value of y:

$y=-4x+ 33\\y=-4(6)+33\\y=-24+33\\y=9$

thus, the solution of the system is:

$x=6\\y=9$