Question

Use substitution to solve the system of equations:

a) x + 2y = 1, 2x + 5y = 3
b) x = ____, y = ____

Answer 1

To solve the system of equations using the substitution method, choose one of the equations and solve it for one variable in terms of the other. Substitute the expression for that variable into the other equation and solve for the remaining variable. Finally, substitute the value of the remaining variable back into one of the original equations to solve for the other variable.

Step-by-step explanation:

To solve the system of equations using the substitution method, follow these steps:

1. Choose one of the equations and solve it for one variable in terms of the other.
2. Substitute the expression for that variable into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the found value of the remaining variable back into one of the original equations to solve for the other variable.

Using these steps, we can solve the given system of equations:

a) x + 2y = 1, 2x + 5y = 3

From the first equation, solve for x:

x = 1 - 2y

Substitute this expression for x into the second equation:

2(1 - 2y) + 5y = 3

Simplify and solve for y:

-4y + 2 + 5y = 3

y = 1

Substitute the value of y back into the first equation to solve for x:

x + 2(1) = 1

x = -1

Therefore, the solution to the given system of equations is x = -1, y = 1.