4x+5y=11 2x+6y=16 solve algebraically
2 x + 6 y = 16 Multiply both sides by 2
4 x + 5 y = 11
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4 x + 12 y = 32
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4 x - 4 x + 5 y - 12 y = 11 - 32
- 7 y = - 21 Divide both sides by - 7
y = - 21 / - 7
y = 3
Replace value of y in equation :
4 x + 12 y = 32
4 x + 12 * 3 = 32
4 x + 36 = 32 Subtract 36 to both sides
4 x + 36 - 36 = 32 - 36
4 x = - 4 Divide both sides by 4
x = - 4 / 4
x = - 1
The solutions are :
x = - 1 , y = 3
You can write this like :
( - 1 , 3 )
To solve the system of equations algebraically, we can use the method of substitution or elimination. Let's use the method of elimination:
Step 1: Multiply the second equation by -2 to make the coefficients of x in both equations the same:
-2(2x+6y) = -2(16)
-4x - 12y = -32 (equation 3)
Step 2: Add equation 1 and equation 3 together to eliminate the term with x:
(4x+5y) + (-4x-12y) = 11 + (-32)
-7y = -21
Step 3: Divide both sides of the equation by -7 to solve for y:
-7y/-7 = -21/-7
y = 3
Step 4: Substitute the value of y back into one of the original equations (let's use equation 1) to solve for x:
4x + 5(3) = 11
4x + 15 = 11
4x = 11 - 15
4x = -4
x = -1
So, the solution to the system of equations is x = -1 and y = 3.
To solve the given system of equations algebraically, we can use either the substitution method or the elimination method. For this example, we'll use the elimination method:
Step 1: Multiply both sides of the first equation by 2 to make the x terms have the same coefficient:
2(4x + 5y) = 2(11)
8x + 10y = 22
Step 2: Multiply both sides of the second equation by -4 to make the x terms have opposite coefficients:
-4(2x + 6y) = -4(16)
-8x - 24y = -64
Step 3: Add the two equations together:
(8x + 10y) + (-8x - 24y) = 22 + (-64)
8x - 8x + 10y - 24y = -42
-14y = -42
Step 4: Divide both sides by -14 to isolate y:
-14y / -14 = -42 / -14
y = 3
Step 5: Substitute the value of y back into one of the original equations. Let's use the first equation:
4x + 5(3) = 11
4x + 15 = 11
4x = 11 - 15
4x = -4
x = -4 / 4
x = -1
So the solution to the system of equations is x = -1 and y = 3.