The system of equations below has multiple solutions, all of which satisfy the equation 𝑦=43𝑥−2. If it can be determined, what is the value of a ? 8x-6y= 1212x-ay = 18
Question
The system of equations below has multiple solutions, all of which satisfy the equation 𝑦=43𝑥−2. If it can be determined, what is the value of a ? 8x-6y= 1212x-ay = 18
Solution
To find the value of 'a', we first need to express the first equation in terms of y.
The first equation is 8x - 6y = 12.
We can rearrange this to find y in terms of x:
6y = 8x - 12 y = (8/6)x - 12/6 y = (4/3)x - 2
We know from the problem statement that y = 43x - 2.
So, we can set these two equations equal to each other:
(4/3)x - 2 = 43x - 2
Solving for x gives us x = 0.
Substituting x = 0 into the equation y = 43x - 2 gives us y = -2.
Now we can substitute x = 0 and y = -2 into the second equation to find the value of 'a':
12x - ay = 18 120 - a(-2) = 18 2a = 18 a = 18 / 2 a = 9
So, the value of 'a' is 9.
Similar Questions
Find the solution of the system of equations.8, x, minus, 10, y, equals, 288x−10y=284, x, minus, y, equals, 64x−y=6
What number of solutions would this system of equations have?𝑦=6𝑥+2y=6x+2−2𝑦=−12𝑥−4−2y=−12x−4
For what value of a would the following system of equations have an infinite number of solutions?x - 2y = 83x - 6y = 4a
For what value of a would the following system of equations have infinitely many solutions?x - 2y = 153x - 6y = 5a
Which of these systems of equations have a solution of (6, -2)? Select all that apply.2x+5y=2–2x+3y=–18y=–x+4y=–13xy=23x–63x+10y=–2y=x+8y=2x–14y=12x–5x–y=4x+2y=2x–3y=12Submit
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.