Solve a system of equations using substitution

Learning Objectives Identify a system of two linear equations. Isolate a variable in one of the equations. Substitute an algebraic expression into the second equation. Solve the resulting single-variable linear equation. Find the value of the second variable by substituting back into an original equation. Write the solution to a system of equations as an ordered pair (x, y). Verify their solution by substituting it into both original equations. Ever wonder how to find the exact point where two different paths cross? 🗺️ Or when two different phone plans cost the same amount? 🤔 In this lesson, you'll learn a powerful algebraic technique called substitution to solve systems of linear equations. This method helps us find the unique point (if it exists!) where two lines...

TermDefinitionExample System of Linear EquationsTwo or more linear equations that share the same variables. We are looking for values of the variables that satisfy ALL equations simultaneously.$$y = 2x + 1$$ $$y = -x + 4$$ Solution to a SystemAn ordered pair (x, y) that makes ALL equations in the system true when substituted into them. Graphically, it's the point where the lines intersect.For the system $y=x+1$ and $y=2x-1$, the solution is (2, 3) because $3=2+1$ and $3=2(2)-1$ are both true. Substitution MethodAn algebraic technique for solving systems of equations by solving one equation for one variable, and then substituting that expression into the other equation.If $y = x + 3$, you can substitute 'x + 3' for 'y' in another equation like $2x + y = 7$, making...

The Substitution Method Steps 1. Solve one of the equations for one of its variables (e.g., solve for y in terms of x, or x in terms of y). 2. Substitute the expression from Step 1 into the OTHER equation. 3. Solve the resulting single-variable equation for that variable. 4. Substitute the value found in Step 3 back into one of the original equations (or the equation from Step 1) to find the value of the second variable. 5. Write your solution as an ordered pair (x, y). 6. Check your solution by substituting the ordered pair into BOTH original equations. This is the step-by-step procedure to follow when using the substitution method to solve a system of two linear equations. Always remember to substitute into the *other* equation in Step 2. Solution Verification Rule An ordere...