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Is the point (5,8) a solution to the system of equations shown below? Justify your response

the system of equation is: 4x+y=28
x-y=3

User Hanlin
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2 Answers

4 votes

Final answer:

The point (5,8) is not a solution to the system of equations because it only satisfies one of the two equations. For a point to be a solution, it must satisfy all equations in the system.

Step-by-step explanation:

The student asked if the point (5,8) is a solution to the system of equations consisting of 4x + y = 28 and x - y = 3. To justify the response, we will substitute the x-coordinate and y-coordinate of the point (5,8) into both equations to see if they hold true.

For the first equation, 4x + y = 28, substituting (5,8) gives us 4(5) + 8, which equals 20 + 8; hence, our equation becomes 28 = 28, which is true.

For the second equation, x - y = 3, substituting (5,8) gives us 5 - 8, which is -3; therefore, the equation becomes -3 = 3, which is false.

As (5,8) satisfies only one of the two equations, it is not a solution to the system of equations. A point must satisfy all equations within a system to be considered a solution.

User Fhnaseer
by
4.7k points
5 votes

Step-by-step explanation:

For the point (5,8) to be a solution to the equations, when you insert x=5 and y=8 , they have to equal to the given values

substituting (5,8) into 4x+y

4(5)+8

=20+8

=28

substituting(5,8) into x-y=3

5-8

= -3

User Jos Woolley
by
5.1k points