What is substitution in algebra?

Substitution in algebra is a method used to replace a variable with a given value or another expression. This allows for simplification of equations and helps in solving for unknown variables.

How do you use substitution to solve the system of equations: x + y = 10 and y = 2x?

First, substitute the expression for y from the second equation into the first equation: x + 2x = 10. This simplifies to 3x = 10, so x = 10/3. Now, substitute x back into the equation y = 2x: y = 2(10/3) = 20/3.

Given the equation y = 3x + 1, what is y when x = 4? Use substitution to find the answer.

Substitute x = 4 into the equation: y = 3(4) + 1 = 12 + 1 = 13. Therefore, y = 13.

Solve for x using substitution: 2x + 3y = 12 and y = x - 1. What is the value of x?

Substitute y = x - 1 into the first equation: 2x + 3(x - 1) = 12. This simplifies to 2x + 3x - 3 = 12, or 5x - 3 = 12. Adding 3 to both sides gives 5x = 15, so x = 3.

If f(x) = 2x² + 3 and you need to find f(5) using substitution, what is the result?

Substitute x = 5 into the function: f(5) = 2(5)² + 3 = 2(25) + 3 = 50 + 3 = 53. Therefore, f(5) = 53.

Use substitution to find the value of y in the equation 4x + 5y = 20, if x = 2.

Substitute x = 2 into the equation: 4(2) + 5y = 20. This simplifies to 8 + 5y = 20. Subtracting 8 from both sides gives 5y = 12, so y = 12/5.

Consider the system of equations: 3x + 2y = 6 and x = y + 1. Find the value of y using substitution.

Substitute x = y + 1 into the first equation: 3(y + 1) + 2y = 6. This simplifies to 3y + 3 + 2y = 6, or 5y + 3 = 6. Subtracting 3 from both sides gives 5y = 3, so y = 3/5.

If you have the equation x = 2y + 4 and you need to find y when x = 10, how would you do it?

Substitute x = 10 into the equation: 10 = 2y + 4. Subtracting 4 from both sides gives 6 = 2y. Dividing both sides by 2 gives y = 3.