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Answer: The gradient of the line segment between the points (-5,2) and (4,3) is .
Step-by-step explanation:
Formula for gradient of a line segment :
Given points of the line segment: (-5,2) and (4,3)
Therefore , the gradient of the line segment between the points (-5,2) and (4,3) is .
<u>ANSWER: </u>
The solution of the two equations 2x+3y=5 and 4x - y=17 is (4, -1).
<u>SOLUTION: </u>
Given, two linear equations are 2x + 3y = 5 → (1) and 4x – y = 17 → (2).
Let us first solve the above equations using <em>elimination process. </em>
For elimination, one of the coefficients of variables has to be same in order to cancel them.
Now solve (1) and (2)
eqn (1) 2 → 4x + 6y = 10
eqn (2) → 4x – y = 17
(-) ----------------------------
0x + 7y = -7
y = -1
Substitute y value in (2)
So, solution of two equations is (4, -1).
<u><em>Now let us solve using substitution process.</em></u>
Then, (2) → 4x – y = 17 → 4x = 17 + y → y = 4x – 17
Now substitute y value in (1) → 2x + 3(4x – 17) = 5 → 2x + 12x – 51 = 5 → 14x = 5 + 51 → 14x = 56
x = 4
Substitute x value in (2) → y = 4(4) – 17 → y = 16 – 17 → y = -1
Hence, the solution of the two equations is (4, -1).