What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify...
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![Page 1: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/1.jpg)
What is the slope of the line that passes through the following points.
1. (-2 , 5) (1 , 4) Identify the slope and y-intercept of each
equation. 2. y = 6x + 8 3. 3x + 4y = -24 4. 2y = 8 Graph the following equations: 5. y = 2x + 3
![Page 2: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/2.jpg)
1. Find the y-intercept of the following equation 3x = 18 + 2y
2. Tell whether the two equations are parallel lines.
5y + 2x = 12 ; 4y = 10y – 4
3. Find the solution to the system2x + y = 4x - y = 2
![Page 3: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/3.jpg)
The student will be able to:
solve systems of equations using substitution.
![Page 4: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/4.jpg)
You can solve a system of equations using different methods. The idea is to determine which method is easiest for that particular problem.
These notes show how to solve the system algebraically using SUBSTITUTION.
![Page 5: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/5.jpg)
Step 1: Solve an equation for one variable.
Step 2: Substitute
Step 3: Solve the equation.
Step 4: Plug back in to find the other variable.
Step 5: Check your solution.
Pick the easier equation. The goal
is to get y= ; x= ; a= ; etc.
Put the equation solved in Step 1
into the other equation.
Get the variable by itself.
Substitute the value of the variable
into the equation.
Substitute your ordered pair into
BOTH equations.
![Page 6: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/6.jpg)
![Page 7: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/7.jpg)
x + y = 5y = 3 + x
Step 1: Solve an equation for one variable.
Step 2: Substitute
The second equation is
already solved for y!
x + y = 5x + (3 + x) = 5
Step 3: Solve the equation.
2x + 3 = 5
2x = 2
x = 1
![Page 8: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/8.jpg)
x + y = 5y = 3 + x
Step 4: Plug back in to find the other variable.
x + y = 5
(1) + y = 5
y = 4
Step 5: Check your solution.
(1, 4)
(1) + (4) = 5
(4) = 3 + (1)
The solution is (1, 4). What do you think the answer would be if you graphed the two equations?
![Page 9: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/9.jpg)
1. (2, 2)2. (5, 3)3. (3, 5)4. (3, -5)
3x – y = 4x = 4y - 17
![Page 10: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/10.jpg)
3y + x = 74x – 2y = 0
Step 1: Solve an equation for one variable.
Step 2: Substitute
It is easiest to solve the
first equation for x.
3y + x = 7
-3y -3y
x = -3y + 7
4x – 2y = 0
4(-3y + 7) – 2y = 0
![Page 11: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/11.jpg)
3y + x = 74x – 2y = 0
Step 4: Plug back in to find the other variable.
4x – 2y = 0
4x – 2(2) = 0
4x – 4 = 0
4x = 4
x = 1
Step 3: Solve the equation.
-12y + 28 – 2y = 0-14y + 28 = 0
-14y = -28y = 2
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3y + x = 74x – 2y = 0
Step 5: Check your solution.
(1, 2)
3(2) + (1) = 7
4(1) – 2(2) = 0
When is solving systems by substitution easier to do than graphing?
When only one of the equations has a variable already isolated (like in example #1).
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1. -4y + 42. -2y + 23. -2x + 44. -2y+ 22
2x + 4y = 43x + 2y = 22
![Page 14: What is the slope of the line that passes through the following points. 1.(-2, 5) (1, 4) Identify the slope and y -intercept of each equation. 2.y.](https://reader034.fdocuments.in/reader034/viewer/2022051821/5697bfbd1a28abf838ca1ec8/html5/thumbnails/14.jpg)
x = 3 – y x + y = 7
Step 1: Solve an equation for one variable.
Step 2: Substitute
The first equation is
already solved for x!
x + y = 7
(3 – y) + y = 7
Step 3: Solve the equation.
3 = 7
The variables were eliminated!!
This is a special case.
Does 3 = 7? FALSE!
When the result is FALSE, the answer is NO SOLUTIONS.
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2x + y = 4 4x + 2y = 8
Step 1: Solve an equation for one variable.
Step 2: Substitute
The first equation is
easiest to solved for y!
y = -2x + 44x + 2y = 8
4x + 2(-2x + 4) = 8
Step 3: Solve the equation.
4x – 4x + 8 = 8
8 = 8This is also a special case.
Does 8 = 8? TRUE!
When the result is TRUE, the answer is INFINITELY MANY SOLUTIONS.
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1. The lines intersect2. The lines are parallel3. The lines are coinciding4. The lines reciprocate5. I can spell my name