Lesson Systems of Equations II: Solving Algebraically

Lesson: Systems of Equations II

Solving Algebraically

Multiple Select

What are the possible solutions to a system of equations? CHOOSE ALL THAT APPLY

• One solution

• Three solutions

• No solutions

• Infinitely many solutions

​Think about it....














What is the solution for this system of equations?

​5y - 2x cannot be both 12 and -4 at the same time.

Therefore, there is no solution to this system of equations.

​https://www.ixl.com/math/grade-8/solve-a-system-of-equations-using-substitution

​On the provided graph, use the intercept method to graph each of these lines.

Be sure to use a straight edge!

The solution to this system of equations is where the two lines connect, or intersect, one another.

On the next slide, you will enter the solution.

Fill in the Blank

What is the solution to the system of equations?

​If you don't find the solution by graphing, you can find it algebraically. You can do this by substitution.

3x + 4y = 26
y = 2x + 1

I will substitute 2x + 1 for y in the first equation.
3x + 4y = 26
3x + 4 (2x + 1) = 26

Then, I have to solve for x. I'll save you the work! x = 2

I use x = 2 to find the value for y. So, when x=2, y=5
y = 2x + 1 (2,5) is my coordinate pair.
y = 2 (2) + 1
y = 5 Note: always substitute the pair back in to check.

Fill in the Blank

Find the coordinate pair that is a shared solution for the system of equations.

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,

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Fill in the Blank

Type the coordinate pair that is a solution for this system of equations. (You may use decimals)

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​Congratulations! You just learned a new skill! Now, go to IXL and practice this skill:

https://www.ixl.com/math/grade-8/solve-a-system-of-equations-using-substitution