An equivalent equation has been written by multiplying the second equation by 22.4xโ9y=74๐ฅโ9๐ฆ=7โโ4xโ9y=74๐ฅโ9๐ฆ=72(โ2x+3y=4)2(โ2๐ฅ+3๐ฆ=4)โโโ4x+6y=8โ4๐ฅ+6๐ฆ=8What is the solution to the system?Responses(โ5,โ192)negative 5 comma negative 19 halves(โ152,โ113)negative 15 halves comma negative 11 thirds(โ1910,ย 115)negative 19 tenths comma 1 fifteenth(โ192,โ5)
Question
An equivalent equation has been written by multiplying the second equation by 22.4xโ9y=74๐ฅโ9๐ฆ=7โโ4xโ9y=74๐ฅโ9๐ฆ=72(โ2x+3y=4)2(โ2๐ฅ+3๐ฆ=4)โโโ4x+6y=8โ4๐ฅ+6๐ฆ=8What is the solution to the system?Responses(โ5,โ192)negative 5 comma negative 19 halves(โ152,โ113)negative 15 halves comma negative 11 thirds(โ1910,ย 115)negative 19 tenths comma 1 fifteenth(โ192,โ5)
Solution
The given system of equations is:
4x - 9y = 7 -4x + 6y = 8
To solve this system of equations, we can use the method of addition (also known as the method of elimination). This method involves adding the two equations together in order to eliminate one of the variables.
Adding the two equations gives:
4x - 9y + -4x + 6y = 7 + 8 0x - 3y = 15 -3y = 15 y = 15 / -3 y = -5
Substitute y = -5 into the first equation:
4x - 9(-5) = 7 4x + 45 = 7 4x = 7 - 45 4x = -38 x = -38 / 4 x = -19/2
So, the solution to the system of equations is x = -19/2 and y = -5, which corresponds to the first option (-5, -19/2).
Similar Questions
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Instructions: Solve each system by substitution. Make sure to check your answer BEFORE submitting. State your answer as an ordered pair. DO NOT include spaces in your answer.System 1โ2xโ3y=โ2โ2๐ฅโ3๐ฆ=โ2ย y=2x+14๐ฆ=2๐ฅ+14(( ,, ))System 2โ3xโ3y=9โ3๐ฅโ3๐ฆ=9ย y=4๐ฆ=4(( ,, )
Instructions: Solve each system by substitution. Make sure to check your answer BEFORE submitting. State your answer as an ordered pair. DO NOT include spaces in your answer.System 1y=โ5x+13๐ฆ=โ5๐ฅ+13y=โ2x+7๐ฆ=โ2๐ฅ+7(( ,, ))System 2y=โ4xโ12๐ฆ=โ4๐ฅโ12y=7x+21๐ฆ=7๐ฅ+21(( ,, )
What is the solution to the system of equations?y=12xโ6๐ฆ=12๐ฅโ6x=โ4๐ฅ=โ4Responses(โ8,โ4)negative 8 comma negative 4(4,โ4)4 comma negative 4(โ4,โ8)negative 4 comma negative 8(โ4,ย 4)
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