Solving with Substitution
objectives
- Solve systems of equations with substitution - Apply solving systems with substitution to real world scenarios - Identify systems of equations with special solutions.
Next
Why not just stick with graphing?
Next
substitution!
Next
Until now, you have been substituting a constant in for a variable. If a variable equals an expression, you can substitute the entire expression in for that variable!
5x + 3y - 11 Find y if x = 4y +3
zoom poll
Next
Until now, you have been substituting a constant in for a variable. If a variable equals an expression, you can substitute the entire expression in for that variable!
5x + 3y - 11 Find y if x = -2y + 1 a) -7y + 5 b) -7y - 6 c) 13y - 6
y = 8 - 3x3x + 2y = 13
How it's done
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
-2y + 4 = x4x - 3y = -6
How it's done
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
3x - y = -72x + y = 2
How it's done
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
Your Turn!
next
back
Your Turn!
next
back
Your Turn!
next
back
How it's done
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
Dana's team is selling hoagies and pizzas for a fundraiser.Hoagies cost $9. Pizzas cost $8. The team sells 99 total items and makes a total of $810. Write and solve a system of equations to find out how many of each item they sold.
next
back
Why not just stick with graphing?
Next
Jake earns $8 per hour washing cars. He earns $10 per hour babysitting.This week he worked 15 hours and earned $140. How many hours did Jake work at each job?
next
back
Special solution!
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
Special solution!
3x - 4y = 126x - 8y = 24
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
remember your cfu in edio!
You should be able to
- Solve systems of equations with substitution - Apply solving systems with substitution to real world scenarios - Identify systems of equations with special solutions.
back
Systems with Substitution
HS: High School
Created on October 7, 2024
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Transcript
Solving with Substitution
objectives
- Solve systems of equations with substitution - Apply solving systems with substitution to real world scenarios - Identify systems of equations with special solutions.
Next
Why not just stick with graphing?
Next
substitution!
Next
Until now, you have been substituting a constant in for a variable. If a variable equals an expression, you can substitute the entire expression in for that variable!
5x + 3y - 11 Find y if x = 4y +3
zoom poll
Next
Until now, you have been substituting a constant in for a variable. If a variable equals an expression, you can substitute the entire expression in for that variable!
5x + 3y - 11 Find y if x = -2y + 1 a) -7y + 5 b) -7y - 6 c) 13y - 6
y = 8 - 3x3x + 2y = 13
How it's done
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
-2y + 4 = x4x - 3y = -6
How it's done
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
3x - y = -72x + y = 2
How it's done
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
Your Turn!
next
back
Your Turn!
next
back
Your Turn!
next
back
How it's done
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
Dana's team is selling hoagies and pizzas for a fundraiser.Hoagies cost $9. Pizzas cost $8. The team sells 99 total items and makes a total of $810. Write and solve a system of equations to find out how many of each item they sold.
next
back
Why not just stick with graphing?
Next
Jake earns $8 per hour washing cars. He earns $10 per hour babysitting.This week he worked 15 hours and earned $140. How many hours did Jake work at each job?
next
back
Special solution!
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
Special solution!
3x - 4y = 126x - 8y = 24
Step 1: Isolate a variable. Step 2: Whatever that variable equals, substitute into the other equation. Now you only have one variable in an equation Step 3: Solve for the remaining variable. Step 4: Substitute the value of that variable into the first equation. Step 5: Write the solution as an ordered pair. Step 6: Verify!
next
back
remember your cfu in edio!
You should be able to
- Solve systems of equations with substitution - Apply solving systems with substitution to real world scenarios - Identify systems of equations with special solutions.
back