Step 1) Solve the first equation for yy:
0.05x + 0.25y = 660.05x+0.25y=66
-color(red)(0.05x) + 0.05x + 0.25y = -color(red)(0.05x) + 66−0.05x+0.05x+0.25y=−0.05x+66
0 + 0.25y = -0.05x + 660+0.25y=−0.05x+66
0.25y = -0.05x + 660.25y=−0.05x+66
color(red)(4) xx 0.25y = color(red)(4)(-0.05x + 66)4×0.25y=4(−0.05x+66)
1y = (color(red)(4) xx -0.05x) + (color(red)(4) xx 66)1y=(4×−0.05x)+(4×66)
y = -0.2x + 264y=−0.2x+264
Step 2) Substitute (-0.2x + 264)(−0.2x+264) for yy in the second equation and solve for xx:
0.15x + 0.05y = 720.15x+0.05y=72 becomes:
0.15x + 0.05(-0.2x + 264) = 720.15x+0.05(−0.2x+264)=72
0.15x + (0.05 xx -0.2x) + (0.05 xx 264) = 720.15x+(0.05×−0.2x)+(0.05×264)=72
0.15x + (-0.01x) + 13.2 = 720.15x+(−0.01x)+13.2=72
0.15x - 0.01x + 13.2 = 720.15x−0.01x+13.2=72
(0.15 - 0.01)x + 13.2 = 72(0.15−0.01)x+13.2=72
0.14x + 13.2 = 720.14x+13.2=72
0.14x + 13.2 - color(red)(13.2) = 72 - color(red)(13.2)0.14x+13.2−13.2=72−13.2
0.14x + 0 = 58.80.14x+0=58.8
0.14x = 58.80.14x=58.8
(0.14x)/color(red)(0.14) = 58.8/color(red)(0.14)0.14x0.14=58.80.14
(color(red)(cancel(color(black)(0.14)))x)/cancel(color(red)(0.14)) = 420
x = 420
Step 3) Substitute 420 for x in the solution to the first equation at the end of Step 1 and calculate y:
y = -0.2x + 264 becomes:
y = (-0.2 xx 420) + 264
y = -84 + 264
y = 180
The Solution Is: x = 420 and y = 180 or (420, 180)
