Solving System of Equations with Multiplication

Authored by Anthony Clark

Mathematics

9th Grade

Solving System of Equations with Multiplication

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Solve the system using Multiplication.
2x + 3y = 12
5x - y = 13

x = -3, y = -2

x = 1.5, y = 2

x = 6, y = 0

x = 3, y = 2

MULTIPLE CHOICE QUESTION

1 min • 12 pts

Solve for x and y
3x + 2y = 16
7x + y = 19

(-2,5)

(-2,-5)

(2,-5)

(2,5)

DRAG AND DROP QUESTION

1 min • 5 pts

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4( (a) )-2 (b) =-6
36- (c) y-2y= (d)
36- (e) =-6

9-3y

-6

14y

10y

x+3y

24y

DRAG AND DROP QUESTION

1 min • 2 pts

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4(9-3y)-2y =-6
36-12y-2y=-6
36-14y =-6
-14y= (a)
y= (b)

-42

-3

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Find the solution:
2x-5y=15
3x+y=31

(10,1)

(13, -8)

(-10,-7)

No Solution

MULTIPLE CHOICE QUESTION

1 min • 1 pt

−6x + 6y = 0
9x − 8y = 4

(4, −9)

Infinite number of solutions

(−9, 4)

(4, 4)

REORDER QUESTION

1 min • 5 pts

Put the steps for solving by ELIMINATION in order:

Subtract the equations to eliminate one variable

Plug that number into either original equation and solve for the other variable

Make sure the equations are lined up

Solve for the remaining variable

Multiply one or both equations by a number to get common but opposite coefficients

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Solving System of Equations with Multiplication

Solve the system using Multiplication.
2x + 3y = 12
5x - y = 13

Solve for x and y
3x + 2y = 16
7x + y = 19

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4( (a) )-2 (b) =-6
36- (c) y-2y= (d)
36- (e) =-6

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4(9-3y)-2y =-6
36-12y-2y=-6
36-14y =-6
-14y= (a)
y= (b)

Find the solution:
2x-5y=15
3x+y=31

−6x + 6y = 0
9x − 8y = 4

Put the steps for solving by ELIMINATION in order:

Consider the system
4x+3y=-1
5x+4y=1
Let's say I want to eliminate the y's. What is the least common multiple of 3 and 4?
LCM = (a)
Multiply each equation by a number so that the coefficient of y will be 12, with one positive and one negative.
(b) (4x+3y=-1)
(c) (5x+4y=1)

Consider the system
4x+3y=-1
5x+4y=1
After we do this multiplication, what will the new equations be?
4(4x+3y=-1) ---> (a) x + (b) y= (c)
-3(5x+4y=1) ---> (d) x - (e) y= -3

Consider the system:
4x+3y=-1
5x+4y=1
Which we converted to:
16 x + 12y=-4
-15x - 12y= -3
Combining the equations straight down gives us:
(a) x+ (b) y= (c)
Solving for x, we get x= (d)

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Solving System of Equations with Multiplication

Solve the system using Multiplication. 2x + 3y = 125x - y = 13

Solve for x and y3x + 2y = 167x + y = 19

In this systemx+3y=94x-2y=-6it'll be easiest to start by solving the first equation for x.The result of doing so is x=​9-3y.Fill in the blanks to plug that expression in and solve for y:4(​ (a) )-2​ (b) =-636-​ (c) y-2y=​ (d) 36-​ (e) =-6

In this systemx+3y=94x-2y=-6it'll be easiest to start by solving the first equation for x.The result of doing so is x=​9-3y.Fill in the blanks to plug that expression in and solve for y:4(​9-3y)-2​y =-636-​12y-2y=​-636-​14y =-6-14y=​ (a) y=​ (b)

Find the solution:2x-5y=153x+y=31

−6x + 6y = 09x − 8y = 4

Put the steps for solving by ELIMINATION in order:

Consider the system4x+3y=-15x+4y=1Let's say I want to eliminate the y's. What is the least common multiple of 3 and 4?LCM = ​ (a) Multiply each equation by a number so that the coefficient of y will be 12, with one positive and one negative.​ (b) (4x+3y=-1)​ (c) (5x+4y=1)

Consider the system4x+3y=-15x+4y=1After we do this multiplication, what will the new equations be?​ 4(4x+3y=-1) ---> ​ (a) x +​ (b) y=​ (c) ​-3(5x+4y=1)​ ---> ​ (d) x -​ (e) y= -3

Consider the system:4x+3y=-15x+4y=1Which we converted to:16 x +​ 12y=​-4-15x -​ 12y= -3Combining the equations straight down gives us:​ (a) x+​ (b) y=​ (c) Solving for x, we get x=​ (d)

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Solve the system using Multiplication.
2x + 3y = 12
5x - y = 13

Solve for x and y
3x + 2y = 16
7x + y = 19

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4( (a) )-2 (b) =-6
36- (c) y-2y= (d)
36- (e) =-6

In this system
x+3y=9
4x-2y=-6
it'll be easiest to start by solving the first equation for x.
The result of doing so is x=9-3y.
Fill in the blanks to plug that expression in and solve for y:
4(9-3y)-2y =-6
36-12y-2y=-6
36-14y =-6
-14y= (a)
y= (b)

Find the solution:
2x-5y=15
3x+y=31

−6x + 6y = 0
9x − 8y = 4

Consider the system
4x+3y=-1
5x+4y=1
Let's say I want to eliminate the y's. What is the least common multiple of 3 and 4?
LCM = (a)
Multiply each equation by a number so that the coefficient of y will be 12, with one positive and one negative.
(b) (4x+3y=-1)
(c) (5x+4y=1)

Consider the system
4x+3y=-1
5x+4y=1
After we do this multiplication, what will the new equations be?
4(4x+3y=-1) ---> (a) x + (b) y= (c)
-3(5x+4y=1) ---> (d) x - (e) y= -3

Consider the system:
4x+3y=-1
5x+4y=1
Which we converted to:
16 x + 12y=-4
-15x - 12y= -3
Combining the equations straight down gives us:
(a) x+ (b) y= (c)
Solving for x, we get x= (d)