If 2x + 3y = 12 and x + 2y = 10, what is the value of x?

If 2x + 3y = 12 and x + 2y = 10, what is the value of x?

Step 1: Start with the two equations: 2x + 3y = 12 and x + 2y = 10.
Step 2: From the second equation (x + 2y = 10), we want to express x in terms of y. Rearranging gives us x = 10 - 2y.
Step 3: Now, we will substitute the expression for x (10 - 2y) into the first equation (2x + 3y = 12).
Step 4: Substitute: 2(10 - 2y) + 3y = 12.
Step 5: Simplify the left side: 20 - 4y + 3y = 12.
Step 6: Combine like terms: 20 - y = 12.
Step 7: To isolate y, subtract 20 from both sides: -y = 12 - 20.
Step 8: This simplifies to -y = -8, so y = 8.
Step 9: Now that we have y, we can find x. Substitute y = 2 back into the equation x = 10 - 2y.
Step 10: Substitute: x = 10 - 2(2).
Step 11: Simplify: x = 10 - 4, which gives x = 6.

Systems of Linear Equations – The question tests the ability to solve a system of linear equations using substitution.
Substitution Method – The solution involves substituting one variable in terms of another to find the values of both variables.