11. Determine the point of intersection for each pair of lines. Verify
your solution.
x
2 - 5y = 7
x
11 - y
8 = -2
6x - 5y = -12 0.2x - 0.1y = 0.7 13x + 9y = 16
4x + 7y = 23 0.5x - 0.3y = 1.5 5x - 12y = 1
x + 3y = -1 4x - y = 22.
2x + 3y = 9 3x - y = 0.5 4x + 3y = 7.6
x + 5y = 1 2x - 3y = -2 5x - y = -3.8
x - y = -6 -5x + 2y = -1 x + 3y = 31
3x + y = -2 4x - y = 5 3x - 2y = -39
C
A
K
x
2 - y
4 = 3
x
2
3x + - (y + 9) = 0 y
2 = 23
2
x
9
+ y - 3
3 = 1
To find the point of intersection for each pair of lines, we can solve the system of equations using either substitution or elimination method.
1) x + 2 - 5y = 7
x - 5y = 5
6x - 5y = -12
6x = -12 + 5y
6x - 5y = -12
6(5y + 5) - 5y = -12
30y + 30 - 5y = -12
25y = -42
y = -42/25
y = -1.68
Substitute the value of y back into one of the equations:
x - 5(-1.68) = 5
x + 8.4 = 5
x = 5 - 8.4
x = -3.4
The point of intersection is (-3.4, -1.68).
2) 0.2x - 0.1y = 0.7
13x + 9y = 16
Multiply the first equation by 10 to eliminate decimals:
2x - y = 7
13x + 9y = 16
Multiply the first equation by 9 to make the coefficients of y equal and add to eliminate y:
18x - 9y = 63
13x + 9y = 16
Adding the equations gives:
18x - 9y + 13x + 9y = 63 + 16
31x = 79
x = 79/31
x = 2.548
Substitute the value of x back into one of the equations:
2(2.548) - y = 7
5.096 - y = 7
-y = 7 - 5.096
-y = 1.904
y = -1.904
The point of intersection is (2.548, -1.904).
3) 4x + 7y = 23
0.5x - 0.3y = 1.5
Multiply the second equation by 10 to eliminate decimals:
5x - 3y = 15
4x + 7y = 23
Multiply the first equation by -7 to make the coefficients of y equal and add to eliminate y:
-35x + 21y = -105
4x + 7y = 23
Adding the equations gives:
-35x + 21y + 4x + 7y = -105 + 23
-31x + 28y = -82
31x - 28y = 82
Solve this new equation by elimination method to find the values of x and y.
Continuing with the same process for the remaining pairs of lines, we can find the points of intersection for each.