Respuesta :
To answer whether or not the friend is correct, we must solve the system of equations. This can be done by setting the expressions equal to each other:
0.5x + 1 = -x + 7
Next, we combine like terms:
0.5x + 1 = -x + 7 ⇒ 1.5x = 6
Finally, divide by the coefficient (1.5):
6 ÷ 1.5 = 4
Hence, x = 4 is the solution. Your friend is correct.
Answer:
Yes, my friend is correct.
Step-by-step explanation:
To verify if my friend's solution is correct, we can substitute the value of [tex]\sf x = 4[/tex] into both equations and check if the resulting [tex]\sf y[/tex] values satisfy the system of equations:
Equation 1:
[tex]\sf y = 0.5x + 1[/tex]
Substitute x = 4.
[tex]\sf y = 0.5(4) + 1 = 2 + 1 = 3[/tex]
Equation 2:
[tex]\sf y = -x + 7[/tex]
Substitute x = 4.
[tex]\sf y = -(4) + 7 = 3[/tex]
The solution [tex]\sf (x = 4, y = 3)[/tex] satisfies both equations. Therefore, my friend is correct. The system of linear equations is satisfied when [tex]\sf x = 4[/tex].