Step 1) Solve the first equation for yy:
2x + y = 52x+y=5
-color(red)(2x) + 2x + y = -color(red)(2x) + 5−2x+2x+y=−2x+5
0 + y = -2x + 50+y=−2x+5
y = -2x + 5y=−2x+5
Step 2) Substitute (-2x + 5)(−2x+5) for yy in the second equation and solve for xx:
-29 = 5y - 3x−29=5y−3x becomes:
-29 = 5(-2x + 5) - 3x−29=5(−2x+5)−3x
-29 = (5 xx -2x) + (5 xx 5) - 3x−29=(5×−2x)+(5×5)−3x
-29 = -10x + 25 - 3x−29=−10x+25−3x
-29 = -10x - 3x + 25−29=−10x−3x+25
-29 = (-10 - 3)x + 25−29=(−10−3)x+25
-29 = -13x + 25−29=−13x+25
-29 - color(red)(25) = -13x + 25 - color(red)(25)−29−25=−13x+25−25
-54 = -13x + 0−54=−13x+0
-54 = -13x−54=−13x
(-54)/color(red)(-13) = (-13x)/color(red)(-13)−54−13=−13x−13
54/13 = (color(red)(cancel(color(black)(-13)))x)/cancel(color(red)(-13))
54/13 = x
x = 54/13
Step 3) Substitute 54/13 for x in the solution to the first equation at the end of Step 1 and calculate y:
y = -2x + 5 becomes:
y = (-2 xx 54/13) + 5
y = -108/13 + 5
y = -108/13 + (13/13 xx 5)
y = -108/13 + 65/13
y = -43/13
The Solution Is: x = 54/13 and y = -43/13 or (54/13, -43/13)
