Linear Equations in Two Variables Test - 10

For the equation 5x – 7y = 35, if y = 5,

5x−7y = 35

y = 5

5x−7.5 = 35

5x−35 = 35

5x = 35 + 35

5x = 70

x = 70/5 = 14

x = 14

To find the area of the triangle formed by the line 2x + 5y = 10 and co-ordinate axis

we put x = 0 in given equation

at x = 0 we get y = 2

at y = 0 we get x =5

so the line cut y axis at 2 and x axis at 5

so the height of triangle is 2 unit and base is 5 unit

area ot triangle = 1/2 base x height

= 1/2 x 2 x 5

= 5 sq. units

let the cost of apples be Rs x per Kg and cost of grapes be Rs y per Kg The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs.160

so the equation will be

2x+y =160

If (-2, 5) is a solution of 2x + my = 11

then it will satisfy the given equation
2 .(-2)+5 m=11
-4+5 m=11
5 m=11+4
5 m=15
m = 15/5 = 3
m=3

The graph of the equation x + y = 4

Put x=0 cut y axis at y = 4

Put y=0 cut x axis at x = 4

There are many lines pass through the point (2, 14)

for example

x - y = -12
2x + y =18
and many more

Total fare

y = 8.1+ (x-1)5

{where y is total fair and x is the total distance travelled }

y = 8 + 5x - 5

y = 5x+3

when a line cuts x -axis in that case y co-ordinate is 0

so to find the co-ordinate of x we put y = 0 in given equation

x – 5y + 3 = 0

at y = 0

x - 5.0 +3 = 0

x + 3 = 0

x = -3

so the co-ordinate are (-3,0)

y = 5x

at x = 1
y = 5.1 = 5
y = 5
(1,5)

at x = 2
y = 5.2 = 10
y = 10
(2,10)

at x = 3
y = 5.3 = 15
y = 15
(3,15)

Since all the given co- ordinate (1, 2), (-1, -16) and (0, -7) satisfy the given line y = 9x – 7

for point (1,2)
y = 9x - 7
2 = 9.1 - 7
2 = 9 - 7
2 = 2
hence (2,1) is a solution

for point (-1,-16)
y = 9x - 7
-16 = 9.-1 - 7
-16 = -9-7
-16 = -16
hence (-1,-16) is a solution

for point (0,-7)
y = 9x - 7
-7 = 9.0 -7
-7 = -7
hence (0,-7) is a solution