Answer:
x = -8/3 and y = -49/3
Step-by-step explanation:
(Step 1) To solve using substitution, you first need to isolate a variable in one of these equations. I chose to isolate "y" in the following equation.
-8x + y = 5 <--- Original equation
y = 5 + 8x <--- Add 8x to both sides
(Step 2) Now, substitute (5 + 8x) for "y" in the second equation.
5x - y = 3 <--- Original equation
5x - (5 + 8x) = 3 <--- Substitute 5 + 8x for "y"
5x - 5 - 8x = 3 <--- Distribute (-) in the parentheses
-3x - 5 = 3 <--- Combine terms with "x"
-3x = 8 <--- Add 5 to both sides
x = -8/3 <--- Divide both sides by -3
(Step 3) Since you know the value of "x", plug it into one of the equations to solve for "y".
y = 5 + 8x <--- Original (rearranged) equation
y = 5 + 8(-8/3) <--- Plug (-8/3) for "x"
y = 5 - 64/3 <--- Multiply
y = 15/3 - 64/3 <--- Convert 5 into a fraction
y = -49/3 <--- Subtract
(Step 3.5) You can check your work by plugging "y" into the other equation to see if the answer for "x" is the same.
5x - y = 3 <--- Original equation
5(-8/3) - y = 3 <--- Plug (-8/3) for "x"
-40/3 - y = 3 <--- Multiply
-40/3 - y = 9/3 <--- Convert 3 into a fraction
-49/3 - y = 0 <--- Subtract both sides by 9/3
-49/3 = y <--- Add both sides by "y"
The value of the system of equations is x = -8/3 and y = -49/3.
