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2a-b equals 17 3a plus 4b equals -13?
Elimination Method
If you can multiply one of the equations by a number and eliminate one of the variables, that is an easy to find the value of the other variable. I see -b in Eq. #1 and +4b in Eq. #2. I can multiply by Eq. #1 by 4 and add to Eq. #2 eliminate b.
Eq. #1 = 2a - b = 17
Eq. #2 = 3a + 4b = -13
4* (2a - b = 17) = 8a - 4b = 68 Now add 4* Eq. #1 to Eq. #2
..8a - 4b = 68
+.3a + 4b = -13
.11a + 0b = 55
11a = 55 divide both sides by 11
a = 5
Substituting a = 5 into Eq. #1
(2 * 5) - b = 17
10 - b = 17 subtract 10 from both sides
- b = 17 - 10
-b = 7 Divide by -1
b = -7
Check in Eq. #2, by substituting a = 5 and b = -7
3a + 4b = -13
(3 * 5) + (4 * -7) = -13
15 + -28 = -13
-13 = -13
The other way of solving simultaneous equations is Substitution.
Solve for one variable in terms of the other variable.
Eq. #1 = 2a - b = 17
Eq. #2 = 3a + 4b = -13
Solve Eq.#1 for a in terms of b.
2a - b = 17 add +b to both sides
2a = b + 17 divide (b + 17) by 2
a = (b + 17) ÷ 2
Substitute a = (b + 17) ÷ 2 into Eq.#2, and solve for b
Eq. #2 = 3a + 4b = -13
3 * [(b + 17) ÷ 2] + 4b = -13 Multiply 3 * (b + 17)
(3b + 51)÷2 + 4b = -13 Multiply both sides by 2 to eliminate the (÷2)
(3b + 51) + 8b = -26 Add (3b + 8b)
11b + 51 = -26 Add -51 to both sides
11b = -77 Divide both sides by 11
b = -7
Substitute b = -7 into Eq.#1
Eq. #1 = 2a - b = 17
2a + 7 = 17 Subtract 7 from both sides
2a = 10 Divide both sides by 2
a = 5
That Substitution sure was complicated compared to the Elimination method. I wonder if it would have been easier to solve Eq.#1 for a in terms of b. That [(b + 17) ÷ 2] was the trouble maker.
Eq. #1 = 2a - b = 17 Add b to both sides
2a = 17 + b subtract 17 from both sides
2a -17 = b reverse sides
b = 2a - 17
Substitute (b = 2a - 17) into Eq.#2, and solve for a
Eq. #2 = 3a + 4b = -13
3a + 4 * (2a - 17) = -13 Multiply 4 * (2a - 17)
3a + (8a - 68) = -13 Add 3a + 8a
11a - 68 = -13 Add +68 to both sides
11a = 55 Divide by 11
a = 5
Eq. #1 = 2a - b = 17 Substitute a = 5 into Eq.#1
2 * 5 - b = 17 Multiply 2 * 5 = 10
10 - b = 17 Add -10 to both sides
b = -7
We got the same answers as we did by using the elimination method, but the substitution was more work. Sometimes using the elimination method, you have to multiply both equations by 2 different numbers to eliminate a variable, but I still think it is easier.
What else can I help you with?
What is the solution for 10x plus 13 equals 17?
10x + 13 = 17 ie 10x = 17 - 13 so x = 4/10 = 0.4
What does t represent in this equation 3t plus 4 equals t plus 13?
Gather like terms: 3t - t = 13 - 4 ie 2t = 9 so t =4½ Check: 3t = 13½ + 4 = 17½, 4½ +13 = 17½ QED
13 plus 15 plus 17 plus 13 plus 15 plus 17 plus 13 plus 15 plus 17 plus 13 plus 15 plus 17 plus 13 plus 15 plus 17 plus 13 plus 15 plus 17?
The answer is 270. Simply add up all of the numbers arithmetically like you would for two plus two. To make sure the answer is correct, check your work using a calculator.
What numbers equals 20 and what times what is 20?
20 = 400
15b plus 2 - 13 equals 13b plus 6 - 4b?
15b+2-13 = 13b+6-4b 15b-11 = 9b+6 15b-9b = 6+11 6b = 17 b =17/6 or 2 and 5/6
What is 17 plus 15 plus 13?
17 plus 15 plus 13 equals 45.
Negative 17 plus what divided by 8 equals 13?
Negative 17 plus 121 divided by 8 equals 13.
92 plus 6 plus 17 plus 79 plus 13 equals what?
92 + 6 + 17 + 79 + 13 = 207! \(@^0^@)/o(*￣▽￣*)ブヾ(^▽^*)))
What plus 13 equal 30?
To find what plus 13 equals 30, you can set up the equation: ( x + 13 = 30 ). By subtracting 13 from both sides, you find that ( x = 30 - 13 ), which simplifies to ( x = 17 ). Therefore, 17 plus 13 equals 30.
What is the solution for 10x plus 13 equals 17?
10x + 13 = 17 ie 10x = 17 - 13 so x = 4/10 = 0.4
-13 plus 4 plus -8 equals?
-13+4+(-8)= -9+(-8) = -9-8 = -17
What is the solution to 10x plus 13 equals 17?
10x + 13 = 1710x = 17-1310x = 4x = 4/10x = 0.4
What is 26 plus 17 using the common core method using mental math to add?
To add 26 and 17 using the common core method with mental math, you can break the numbers into tens and ones. First, add the tens: 20 (from 26) plus 10 (from 17) equals 30. Next, add the ones: 6 (from 26) plus 7 (from 17) equals 13. Finally, combine the two results: 30 plus 13 equals 43. Thus, 26 plus 17 equals 43.
What is 2 plus 5 plus 3X2 plus 4 plus 2 plus 17 plus 2-13 plus 5 equals?
2 + 5 + (3 x 2) + 4 +2 + 17 + (2 - 13) + 5 = 30
What is 3x plus 4 equals 17?
It is an equation and the value of x is 13/3
92 plus 79 plus 17 plus 13 plus 6 equals?
207..just search your math questions on google.
How can you determine whether the sum of several numbers such as 13 plus 45 plus 24 plus 17 is even or odd without actually calculating the sum?
Even plus even equals even. Odd plus odd equals odd. Odd plus even equals odd. 13 + 45 (odd plus odd) will be even. Even plus 24 will be even. Even plus 17will be odd. 13 + 45 + 24 + 17 will be odd.
