How would you solve this using substitution method
y= 3 + x
2x + y = 8
To solve this system of equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation, y = 3 + x, for y:
y = 3 + x ----(1)
Step 2: Substitute the expression found in step 1 into the other equation.
Replace y in the second equation, 2x + y = 8, with the expression 3 + x:
2x + (3 + x) = 8 ----(2)
Step 3: Simplify and solve the equation obtained in step 2.
Expand the equation (2) by removing the parentheses:
2x + 3 + x = 8
Combine like terms (2x + x = 3x):
3x + 3 = 8
Subtract 3 from both sides of the equation:
3x = 8 - 3
3x = 5
Step 4: Solve for x.
Divide both sides of the equation by 3:
x = 5/3
Step 5: Substitute the value of x back into one of the original equations.
Let's use the first equation, y = 3 + x:
y = 3 + (5/3)
Step 6: Simplify the equation obtained in step 5.
To add fractions, find a common denominator:
y = (9/3) + (5/3)
y = 14/3
Step 7: Check the solution.
Substitute the values of x and y back into the second equation:
2(5/3) + (14/3) = 8
Multiply 2 by 5/3:
10/3 + 14/3 = 8
Combine the fractions:
24/3 = 8
Simplify the left side of the equation:
8 = 8
Since both sides are equal, the solution (x = 5/3, y = 14/3) is correct.