a. (3,4) is only the solution to Equation 1.
(4, 2.5) is the solution to both equations
(5,5) is the solution to Equation 2
(3,2) is not the solution to any equation.
b. No, it is not possible to have more than one (x,y) pair that is solution to both equations
Step-by-step explanation:
a. Decide whether each neither of the equations,
i (3,4)
ii. (4,2.5)
ill. (5,5)
iv. (3,2)
To decide whether each point is solution to equations or not we will put the point in the equations
Equations are:
Equation 1: 6x + 4y = 34
Equation 2: 5x – 2y = 15
<u>i (3,4)
</u>
Putting in Equation 1:
![6(3) + 4(4) = 34\\18+16=34\\34=34\\](https://tex.z-dn.net/?f=6%283%29%20%2B%204%284%29%20%3D%2034%5C%5C18%2B16%3D34%5C%5C34%3D34%5C%5C)
Putting in Equation 2:
![5(3) - 2(4) = 15\\15-8 = 15\\7\neq 15](https://tex.z-dn.net/?f=5%283%29%20-%202%284%29%20%3D%2015%5C%5C15-8%20%3D%2015%5C%5C7%5Cneq%2015)
<u>ii. (4,2.5)</u>
Putting in Equation 1:
![6(4) + 4(2.5) = 34\\24+10=34\\34=34\\](https://tex.z-dn.net/?f=6%284%29%20%2B%204%282.5%29%20%3D%2034%5C%5C24%2B10%3D34%5C%5C34%3D34%5C%5C)
Putting in Equation 2:
![5(4) - 2(2.5) = 15\\20-5 = 15\\15=15](https://tex.z-dn.net/?f=5%284%29%20-%202%282.5%29%20%3D%2015%5C%5C20-5%20%3D%2015%5C%5C15%3D15)
<u>ill. (5,5)</u>
![6(5) + 4(5) = 34\\30+20=34\\50\neq 34](https://tex.z-dn.net/?f=6%285%29%20%2B%204%285%29%20%3D%2034%5C%5C30%2B20%3D34%5C%5C50%5Cneq%2034)
Putting in Equation 2:
![5(5) - 2(5) = 15\\25-10 = 15\\15=15](https://tex.z-dn.net/?f=5%285%29%20-%202%285%29%20%3D%2015%5C%5C25-10%20%3D%2015%5C%5C15%3D15)
<u>iv. (3,2)</u>
![6(3) + 4(2) = 34\\18+8=34\\26\neq 34](https://tex.z-dn.net/?f=6%283%29%20%2B%204%282%29%20%3D%2034%5C%5C18%2B8%3D34%5C%5C26%5Cneq%2034)
Putting in Equation 2:
![5(3) - 2(2) = 15\\15-4 = 15\\11\neq 15](https://tex.z-dn.net/?f=5%283%29%20-%202%282%29%20%3D%2015%5C%5C15-4%20%3D%2015%5C%5C11%5Cneq%2015)
Hence,
(3,4) is only the solution to Equation 1.
(4, 2.5) is the solution to both equations
(5,5) is the solution to Equation 2
(3,2) is not the solution to any equation.
b. Is it possible to have more than one (x, y) pair that is a solution to both
equations?
The simultaneous linear equations' solution is the point on which the lines intersect. Two lines can intersect only on one point. So a linear system cannot have more than one point as a solution
So,
a. (3,4) is only the solution to Equation 1.
(4, 2.5) is the solution to both equations
(5,5) is the solution to Equation 2
(3,2) is not the solution to any equation.
b. No, it is not possible to have more than one (x,y) pair that is solution to both equations
Keywords: Linear equations, Ordered pairs
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