Example 3: Solving systems by substitution | Systems of equations | 8th grade | Khan Academy | Summary and Q&A

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June 15, 2010
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Example 3: Solving systems by substitution | Systems of equations | 8th grade | Khan Academy

TL;DR

Learn how to solve and graph a system of equations by substituting values to find the point of intersection.

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Questions & Answers

Q: How do you solve a system of equations?

To solve a system of equations, you can use substitution by replacing one variable with an expression from another equation. This allows you to find the values of the variables that satisfy both equations simultaneously.

Q: What is the point of intersection in a system of equations?

The point of intersection is the solution to the system of equations. It is the values of the variables that make both equations true when substituted into each equation.

Q: What is the slope-intercept form of an equation?

The slope-intercept form of an equation is y = mx + b, where m is the slope of the line and b is the y-intercept. This form allows for easy graphing and interpretation of the equation.

Q: How do you graph a system of equations?

Graphing a system of equations involves plotting the equations on a coordinate plane. The point of intersection of the two lines represents the solution to the system. Plot the equations using their slopes and y-intercepts to observe where they intersect.

Summary & Key Takeaways

  • To solve a system of equations, substitute one equation into the other to satisfy both constraints.

  • Example equations: y - x = 5 and 9x + 3y = 15.

  • Solve for x by substituting y in the second equation with 5 + x, then solve for y to find the values of x and y that satisfy both equations.

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