WorksheetsSolving System of Equations with Multiplication
Total questions: 20
Worksheet time: 20mins
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
Solve for x and y
3x + 2y = 16
7x + y = 19
(-2,5)
(-2,-5)
(2,-5)
(2,5)
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
y
12
-6
14y
x
10y
x+3y
24y
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
30
-3
Find the solution:
2x-5y=15
3x+y=31
(10,1)
(13, -8)
(-10,-7)
No Solution
−6x + 6y = 0
9x − 8y = 4
(4, −9)
Infinite number of solutions
(−9, 4)
(4, 4)
Put the steps for solving by ELIMINATION in order:
Make sure the equations are lined up
Multiply one or both equations by a number to get common but opposite coefficients
Subtract the equations to eliminate one variable
Solve for the remaining variable
Plug that number into either original equation and solve for the other variable
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)
12
4
-3
3
5
1
-1
-12
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
16
12
-4
-15
3
5
1
-1
-12
-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)
1
0
-7
3
5
-1
-12
-3
Consider the system:
4x+3y=-1
5x+4y=1
Since we now know that x=-7, solve for y:
4( (a) )+3y=-1
(b) +3y=-1
(c) = (d)
y= (e)
-7
-28
3y
27
9
5
7
-12
3
y
To eliminate the x-variable in the system of equations, multiply the second equation by which number?
-3
-2
-1
0
The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, how many of each type of ticket were sold? What of the following systems represent this situation?
S + A = 530
3S + 4A = 1740
S + A = 530
4S + 3A = 1740
S + A = 1740
3S + 4A = 530
S + A = 1740
4S + 3A = 530
________________ are two or more equations that have the same variables and work together.
graphing lines
elimination method
system of equations
table
What would be the first step to solve this system by elimination?
2x+9y= -7
6x-3y= 9
Add the equations
Subtract the equations
Write each equation in slope intercept form.
Multiple the first equation by 3 or -3
Solve this system of equations using elimination with simple multiplication:
(-6, 4)
(-6, 2)
(-6, 3)
(-6, 1)
Solve this system of equations. Choose whether to use addition, subtraction, or simple multiplication:
−6𝑥 + 3𝑦 = −24
6𝑥 − 𝑦 = 20
(-2, 1)
(-3, 2)
(3, -2)
(3, -1)
Solve this system of equations. Choose whether to use addition, subtraction, or simple multiplication:
x - 4y = -12
x + 3y = 2
(4, 2)
(2, 2)
(-4, 4)
(-4, 2)
Solve this system of equations. Choose whether to use addition, subtraction, or simple multiplication:
-4x + 9y = 9
x - 3y = -6
(9, 5)
(-9, 5)
(8, 5)
(-9, -5)
Solve this system of equations using elimination. Choose whether to use addition, subtraction, or multiplication:
4x + 8y = 20
-4x + 2y = -30
(5, -1)
(7, -1)
(3, -1)
(-7, 0)
