Solve the following system of equations graphically:

Shade the region between the lines and the y-axis

3x − 4y = 7

5x + 2y = 3

#### Solution

The given equations are:

3x − 4y = 7 ......(i)

5x + 2y = 3 ........(ii)

Putting x = 0 in equation (i) weget

`=> 3 xx 0 - 4y = 7`

=> y = -7/4

x = 0, y = -7/4

Putting y = 0 in eqaution (i) we get

`=> 3x - 4 xx 0 = 7`

=> x = 7/3

x= 7/3, y = 0

Use the following table to draw the graph.

x | 0 | 7/3 |

y | -7/4 | 0 |

Draw the graph by plotting the two points A(0, -7/4), B(7/3, 0) from table.

5x + 2y = 3 ....(ii)

Putting x = 0 in equation (ii) we get

`=> 5 xx 0 + 2y = 3`

=> y = 2/3

x = 3/5, y = 0

Use the following table to draw the graph

x | 0 | 3/5 |

y | 3/2 | 0 |

Draw the graph by plotting the two points C(0, 3/2) and D(3/5, 0) from table.

The two lines intersect at points of y−axis.

Hence, x = 1and y = -1 is the Solution.