Answer:
[tex]\left(3, \ \dfrac{5}{2}\right)[/tex]
Step-by-step explanation:
We can solve this system of equations:
[tex]\begin{cases}y=-(3/2)x +7 \\y=(1/2)x+1\end{cases}[/tex]
using elimination.
First, we can multiply the second equation by 3:
[tex]3\left[\dfrac{}{}y=(1/2)x+1\dfrac{}{}\right]\ \implies\ 3y = (3/2)x+3[/tex]
Next, we can add it to the first equation:
[tex]\text{ }\ \ \ \ y=(-3/2)x+7\\ \underline{+ \ 3y= (3/2)x\ \ \,+ 3\ } \\ \\ \text{ } \ \ \, 4y = \ \ 0\ \ \ \ \ \ + 10[/tex]
Then, we can solve for y by dividing both sides of the resulting equation by 4:
[tex]y = \dfrac{10}{4}[/tex]
[tex]\boxed{y=\dfrac{5}{2}}[/tex]
Next, we can solve for x by plugging this y-value into one of the original equations:
[tex]\dfrac{5}{2} = \dfrac{1}{2}x + 1[/tex]
↓ subtracting 1 from both sides
[tex]\dfrac{3}{2} = \dfrac{1}{2}x[/tex]
↓ multiplying both sides by 2
[tex]\boxed{3 = x}[/tex]
So, the solution to the system of equations is:
[tex]\boxed{\left(3, \ \dfrac{5}{2}\right)}[/tex]
