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
i (3,4)
Putting in Equation 1:
[tex]6(3) + 4(4) = 34\\18+16=34\\34=34\\[/tex]
Putting in Equation 2:
[tex]5(3) - 2(4) = 15\\15-8 = 15\\7\neq 15[/tex]
ii. (4,2.5)
Putting in Equation 1:
[tex]6(4) + 4(2.5) = 34\\24+10=34\\34=34\\[/tex]
Putting in Equation 2:
[tex]5(4) - 2(2.5) = 15\\20-5 = 15\\15=15[/tex]
ill. (5,5)
[tex]6(5) + 4(5) = 34\\30+20=34\\50\neq 34[/tex]
Putting in Equation 2:
[tex]5(5) - 2(5) = 15\\25-10 = 15\\15=15[/tex]
iv. (3,2)
[tex]6(3) + 4(2) = 34\\18+8=34\\26\neq 34[/tex]
Putting in Equation 2:
[tex]5(3) - 2(2) = 15\\15-4 = 15\\11\neq 15[/tex]
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
Learn more about linear equations at:
- brainly.com/question/10534381
- brainly.com/question/10538663
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