Question
Substitution method
3x+5y=200
y=7x+2
3x+5y=200
y=7x+2
Answers
GPT 3.5
To solve this system of equations using the substitution method, we will substitute the value of "y" from the second equation into the first equation.
Step 1: Substitute y in the first equation with 7x+2 from the second equation.
3x + 5(7x+2) = 200
Step 2: Distribute 5 to the terms inside the parentheses.
3x + 35x + 10 = 200
Step 3: Combine like terms.
38x + 10 = 200
Step 4: Subtract 10 from both sides.
38x = 190
Step 5: Divide both sides by 38 to solve for x.
x = 190/38
x = 5
Step 6: Substitute the value of x back into the second equation to solve for y.
y = 7(5) + 2
y = 35 + 2
y = 37
Therefore, the solution to the system of equations is x = 5 and y = 37.
Step 1: Substitute y in the first equation with 7x+2 from the second equation.
3x + 5(7x+2) = 200
Step 2: Distribute 5 to the terms inside the parentheses.
3x + 35x + 10 = 200
Step 3: Combine like terms.
38x + 10 = 200
Step 4: Subtract 10 from both sides.
38x = 190
Step 5: Divide both sides by 38 to solve for x.
x = 190/38
x = 5
Step 6: Substitute the value of x back into the second equation to solve for y.
y = 7(5) + 2
y = 35 + 2
y = 37
Therefore, the solution to the system of equations is x = 5 and y = 37.