solve the system of equations graphed on the coordinate axes below. \n$y = \\frac{1}{2}x + 8$\n$y = -4x + 8$
solve the system of equations graphed on the coordinate axes below. \n$y = \\frac{1}{2}x + 8$\n$y = -4x + 8$
Answer
Explanation:
Step1: Set equations equal
Since ( y = \frac{1}{2}x + 8 ) and ( y = -4x + 8 ), set ( \frac{1}{2}x + 8 = -4x + 8 ).
Step2: Solve for x
Subtract 8 from both sides: ( \frac{1}{2}x = -4x ). Add ( 4x ) to both sides: ( \frac{1}{2}x + 4x = 0 ). Combine terms: ( \frac{9}{2}x = 0 ), so ( x = 0 ).
Step3: Find y
Substitute ( x = 0 ) into ( y = \frac{1}{2}x + 8 ): ( y = \frac{1}{2}(0) + 8 = 8 ).
Answer:
The solution is ( (0, 8) )