# 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.

## Key Insights

• ❣️ Solving a system of equations involves finding the values of x and y that satisfy both equations.
• 😑 Substitution is a method used to solve a system of equations by replacing one variable with an expression from another equation.
• 😥 The point of intersection in a system of equations is the solution, where both equations are true.
• 😥 Graphing a system of equations helps visualize the solution by identifying the point of intersection on the coordinate plane.
• 😃 Slope-intercept form (y = mx + b) is useful for graphing equations and understanding their slopes and y-intercepts.
• 💱 The slope of a line represents the rate of change, while the y-intercept is the value of y when x is 0.
• 😥 Substituting values into equations and solving algebraically allows for precise determination of the point of intersection.

## Transcript

We're asked to solve and graph this system of equations here. And just as a bit of a review, solving a system of equations really just means figuring out the x and y value that will satisfy both of these equations. And one way to do it is to use one of the equations to solve for either the x or the y, and then substitute for that value in the other... Read More

### 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.