Linear Equations and Inequalities
Solving equations and inequalities is a foundational skill on the SAT. These types of problems involve finding the value of a variable that satisfies a given equation or inequality.
Example 1 (Linear Equation):
Solve for x:
3x + 4 = 19
Step 1: Subtract 4 from both sides:
3x = 15
Step 2: Divide both sides by 3:
x = 5
Example 2 (Inequality):
Solve for x:
4x – 7 > 5
Step 1: Add 7 to both sides:
4x > 12
Step 2: Divide both sides by 4:
x > 3
Systems of Equations
Sometimes, you’ll be asked to solve a system of equations. These problems require you to find values of variables that satisfy both equations simultaneously.
Example:
Solve the system:
2x + y = 10
x – y = 2
Step 1: Solve the second equation for x:
x = y + 2
Step 2: Substitute x = y + 2 into the first equation:
2(y + 2) + y = 10
2y + 4 + y = 10
3y + 4 = 10
3y = 6
y = 2
Step 3: Substitute y = 2 into x = y + 2:
x = 2 + 2 = 4
Solution: x = 4, y = 2