Linear Equations in Two Variables Test - 1

The given linear equation is 7y - 5 = 8x.
Putting the coordinates (-5, -5) in the given equation,
7(-5) - 5 = 8(-5)
-35 - 5 = -40
-40 = -40; which is true.
Thus, (-5, -5) are the coordinates that satisfy 7y - 5 = 8x.

(m, 8) lies on the graph which is represented by the equation of line 8x – 5y = -8.
Thus, putting x = m and y = 8,
8m – 5(8) = -8
8m – 40 = -8
8m = -8 + 40
8m = 32
m = 32 ÷ 8 = 4

The given two equations are 9x + 4y = 38 and 10x + 3y = 35.
Putting x = 2 and y = 5 in both the given equations,
9x + 4y = 38
9 × 2 + 4 × 5 = 38
18 + 20 = 38
38 = 38; which is true.
Thus, (2, 5) satisfies the equation 9x + 4y = 38.

10x + 3y = 35
10 × 2 + 3 × 5 = 35
20 + 15 = 35
35 = 35; which is true.
Thus, (2, 5) satisfies the equation 10x + 3y = 35.

Therefore, (2, 5) is the point that satisfies both the given linear equations 9x + 4y = 38 and 10x + 3y = 35 simultaneously.

The required line meets the y-axis, so the x-coordinate at that point should be equal to 0.
Putting y = -9 in 3x + 2y = -18,
3x + 2 × -9 = -18
3x - 18 = -18
3x = -18 + 18 = 0
x = 0
So, for the line 3x + 2y = -18, x = 0 at y = -9.
Thus, 3x + 2y = -18 would meet the y-axis at -9.

t (in minutes) is the total time taken to roast and k represents every kilogram.
Therefore, the equation formed is:
t = 28k + 30
t – 28k = 30

The equations y = 31 and y = 14 are both parallel to x-axis; hence, they are parallel to each other.