5. The solution of the system of equation is (13 , 14)
6. The solution of the system of equation is (-4 , 2)
Step-by-step explanation:
We using the elimination method to solve a system of equation by
1. Make the coefficients of one variable equal in magnitude and
different in sign
2. Add the equations to eliminate this variable
3. Solve the resulting equation to find the 2nd variable
4. Substitute the value of the 2nd variable in one of the two equations
to find the first variable
Let us do that
5.
∵ 8x - 6y = 20 ⇒ (1)
∵ -16x + 17y = 30 ⇒ (2)
- Multiply equation (1) by 2 to eliminate x
∴ 16x - 12y = 40 ⇒ (3)
- Add equations (2) and (3)
∴ 5y = 70
- Divide both side by 5
∴ y = 14
Substitute the value of y in equation (1) by 14
∵ 8x - 6(14) = 20
∴ 8x - 84 = 20
- Add 84 to both sides
∴ 8x = 104
- Divide both sides by 8
∴ x = 13
The solution of the system of equation is (13 , 14)
6.
∵ -4y - 11x = 36 ⇒ Arrange the terms
∴ -11x - 4y = 36 ⇒ (1)
∵ 20 = -10x - 10y ⇒ Switch the two sides
∴ -10x - 10y = 20 ⇒ (2)
- Multiply equation (1) by 5 and equation (2) by -2 to eliminate y
∴ -55x - 20y = 180 ⇒ (3)
∴ 20x + 20y = -40 ⇒ (4)
- Add equations (3) and (4)
∴ -35x = 140
- Divide both side by -35
∴ x = -4
Substitute the value of x in equation (1) by -4
∵ -11(-4) - 4y = 36
∴ 44 - 4y = 36
- Add 4y to both sides
∴ 44 = 36 + 4y
- Subtract 36 from both sides
∴ 8 = 4y
- Divide both sides by 4
∴ y = 2
The solution of the system of equation is (-4 , 2)
Learn more:
You can learn more about system of equations in brainly.com/question/3739260
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