## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$(4,3)$
Equation 1 has variables isolated - select the substitution method. $y=\displaystyle \frac{1}{2}x+1\qquad$(*) Replace y with $\displaystyle \frac{1}{2}x+1$ in the second equation: $\displaystyle \frac{1}{2}x+1=2\mathrm{x}-5\qquad$ ... and solve for $x$. Multiply with 2 $x+2=4x-10\qquad$ ... add $10-x$ to both sides $12=3x\qquad$ ... divide with 3 $4=x$ Now, back-substitute into (*) $y=\displaystyle \frac{1}{2}(4)+1=2+1=3$ Form an ordered pair $(x,y)$ as the solution to the system $(4,3)$