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Sagot :
Answer:
(0, - 3 )
Step-by-step explanation:
- 5x - 3y - 9 = 0 → (1)
4x - 18y - 54 = 0 → (2)
multiplying (1) by - 6 and adding to (2) will eliminate y
30x + 18y + 54 = 0 → (3)
add (2) and (3) term by term to eliminate y
34x + 0 + 0 = 0
34x = 0 ⇒ x = 0
substitute x = 0 into either of the 2 equations and solve for y
substituting into (2)
4(0) - 18y - 54 = 0
- 18y - 54 = 0 ( add 54 to both sides )
- 18y = 54 ( divide both sides by - 18 )
y = - 3
solution is (0, - 3 )
Answer:
(0, -3)
Step-by-step explanation:
This system of equations consists of two equations. There are 3 main ways to solve a system of equations:
- Graphing (The solution is the point where the two lines intersect)
- Substitution
- Elimination
First, start by having the variables on one side.
[tex]-5x-3y-9=0 \Rightarrow \text{Add 9 to both sides} \Rightarrow -5x-3y=9\\4x-18y-54=0 \Rightarrow \text{Add 54 to both sides} \Rightarrow 4x-18y=54 \Rightarrow \text{Simplify} \Rightarrow 2x-9y=27[/tex]
Solve Using Elimination
This method is the easiest to use in this situation.
In this method, we increase equations by a certain factor in order to eliminate one variable.
We can see that 3y in the first equation can be multiplied by 6 in order to obtain the 18y in the second equation. Therefore, we can multiply the whole first equation by 6:
[tex]-30x-18y=54\\4x-18y=54[/tex]
Now, subtract the two equations to eliminate y.
[tex]-34x=0\\x=0[/tex]
Plug in 0 to x in either of the equations to solve for y:
[tex]-5(0)-3y=9\\0-3y=9\\-3y=9\\ \text{Divide both sides by -3}\\y=-3[/tex]
OR
[tex]4(0)-18y=54\\0-18y=54\\-18y=54\\\text{Divide both sides by -18}\\y=-3[/tex]
Therefore:
(x, y) = (0, -3)
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