Beyonce is solving a system of equations: 2x β 3y = -2
4x + y = 24
She decides to use t...
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Mathematics, 20.02.2021 04:30 audreydalekshed
Beyonce is solving a system of equations: 2x β 3y = -2
4x + y = 24
She decides to use the elimination method to find the solution. She multiplies the second equation by 3 and adds it to the first equation to find 14x = 70, showing her that x = 5. Beyonce finds that y = 4.
Step 3: 4x + y = 24
4(5) + y = 24
20 + y = 24
-20 -20
y = 4
Step 1: 3(4x + y = 24) β 12x + 3y = 72
Step 2: 2x β 3y = -2
Solution: (5, 4)
+ 12x + 3y = 72
14x = 70
β x = 5
Thinking about this process, Beyonce says out loud, βThere are lots of ways I could go about solving this problem. I could do the method above or I could multiply the first equation by -2 and add the second.
Step 3: 4x + y = 24
4x + 4 = 24
-4 -4
4x = 20
x = 5
Step 1: -2(2x β 3y = -2) β -4x + 6y = 4
Solution: (5, 4)
Step 2: -4x + 6y = 4
+ 4x + y = 24
7y= 28
β y = 4
βI seem to find that there is only one solution to the two equations, but I wonder if I will get the same solution if I use a different method?β
Explain how you know that a system of equations has no solution.
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