Jorge used a graph to determine a solution to the following system of equations: x + y = 92 and y = 3x – 4 Jorge’s answer is (67, 25). Is he correct? Explain how to check if his solution is correct without using a graph.

to check the answer, sub in 67 for x and 25 for y in both equations...because for it to be a solution, it has to satisfy both of the equations.

(67,25)...x = 67 and y = 25

x + y = 92
67 + 25 = 92
92 = 92 (correct)

y = 3x - 4
25 = 3(67) - 4
25 = 201 - 4
25 = 197 (incorrect)

so (67,25) is NOT a solution to this system of equations because it does not satisfy both of the equations

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PallaviB PallaviB · Answer 2 · 2022-06-25T14:18:19+02:00

The solution to the given System of equations is not correct.

What is system of equations ?

System of equations is a finite set of equations for which common solutions are sought.

We have,

[tex]x + y = 92[/tex] [tex]........(i)[/tex]

[tex]y = 3x - 4[/tex] [tex]........(ii)[/tex]

And solution to these System of equations is [tex](67,25)[/tex] i.e. [tex]x=67,\ y=25[/tex]

So,

We have to check whether it is correct or not .

So,

We will substitute the values in each equations;

For equations [tex](i)[/tex],

[tex]x + y = 92[/tex]

[tex]67+25=92[/tex]

[tex]92=92[/tex]

So, these values satisfy the first equation.

Now, For equations [tex](ii)[/tex],

[tex]y = 3x - 4[/tex]

[tex]25=67*3-4[/tex]

[tex]25\neq 197[/tex]

But, these values do not satisfy the equations [tex](ii)[/tex].

For solution to be correct these values should satisfy both the equations .

Hence, we can say that the solution to the given System of equations is not correct.

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