Answer:
(-2, 4)
Step-by-step explanation:
One of the equations is already solved for y, so let's solve the other one for y and by the transitive proprerty of equality, if y = y, then what those y's are equal to are equal to each other. Solving the first equation for y:
x + y = 2 so
y = -x + 2
Let's fill that in for y in the second equation. Where
[tex]y=\frac{1}{2}x+5[/tex], making the substitution,
[tex]-x+2=\frac{1}{2}x+5[/tex]
Combining like terms and getting the x on one side and the constant on the other side of the equals sign:
[tex]-\frac{3}{2}x=3[/tex]
The product of a fraction and its reciprocal is 1 so we will multiply both sides by
[tex]-\frac{2}{3}[/tex] to get:
[tex](-\frac{2}{3})(-\frac{3}{2})x=(3)(-\frac{2}{3})[/tex]
and we end up with x = -2.
Now that we know that, we can sub that in for x in either one of the original equations. I chose the first one:
If x + y = 2, then -2 + y = 2
and y = 4
Therefore, the solution set is (-2, 4)
