Solve a system of equations using substitution

Learning Objectives Define a system of linear equations and its solution. Isolate a variable in a linear equation to prepare for substitution. Accurately substitute an algebraic expression into a linear equation. Solve a system of two linear equations in two variables using the substitution method. Verify the solution to a system by checking it in both original equations. Identify if a system has one solution, no solution, or infinitely many solutions based on the algebraic result. Ever compared two different phone plans to see which is cheaper for you? 📱 You're already thinking about systems of equations! This tutorial will teach you the substitution method, a powerful algebraic tool for finding the exact point where two lines intersect without ever needing to graph...

TermDefinitionExample System of Linear EquationsA set of two or more linear equations that share the same variables. We look for a solution that works for all equations in the system.The equations y = 2x + 1 and 3x + 2y = 9 form a system. The variables are x and y. Solution to a SystemAn ordered pair (x, y) that makes all equations in the system true. Geometrically, it's the point where the lines represented by the equations intersect.For the system y = x + 2 and y = -x + 4, the solution is (1, 3) because 3 = 1 + 2 and 3 = -1 + 4 are both true. Substitution MethodAn algebraic technique for solving a system of equations by solving one equation for a variable and then substituting that resulting expression into the other equation.If y = x + 1, you can substitute 'x + 1' for &...

Step 1: Isolate a Variable Choose one equation and solve for either x or y. Look for a variable with a coefficient of 1 or -1 to make this step easier. This step transforms one equation so that a variable is expressed in terms of the other. For example, transforming `2x + y = 5` into `y = 5 - 2x`. Step 2: Substitute and Solve Substitute the expression from Step 1 into the *other* equation. This creates a new equation with only one variable. If you found `y = 5 - 2x` and the other equation is `3x - 2y = 4`, you would substitute to get `3x - 2(5 - 2x) = 4`. Then, solve this new equation for x. Step 3: Back-Substitute Plug the value you found in Step 2 back into the isolated equation from Step 1 to find the value of the other variable. If you found `x = 2` in the previo...