Question

2x - 3y = 9; 2x + y = 13

5x + 2y = -3; x + 5y = 4
(4) sm
1
3
99x + 101y = 499; 101x + 99 y = 501
49x - 57y = 172; 57x - 49y
49y = 252
Let's recall.
1 of a linear equation in two variables​

Answer 1

The linear equation y = 9 + 3x can be graphed by plotting points derived from a table of values, where '9' is the y-intercept and '3' is the slope of the line.

Step-by-step explanation:

The equation y = 9 + 3x represents a linear equation in two variables where y is the dependent variable and x is the independent variable. The term 9 is the y-intercept (b), and 3 is the slope (m) of the line. To graph this equation, we create a table of values by substituting a range of x-values to find the corresponding y-values. These points are then plotted on a coordinate plane to visualize the line.

For example, if x = 0, then y = 9. If x = 1, then y = 12. Continuing this process with more x-values will yield a complete table that can be used to draw the line on a graph. The relationship between x and y is linear because every increase in x by 1 unit results in an increase in y by 3 units, consistent with the slope of 3.

Answer 2

See explanations below

Step-by-step explanation:

Given the simultaneous equations;

2x - 3y = 9... 1

2x + y = 13 ... 2

From 2;

y = 13-2x

Substitute into 1;

2x - 3(13-2x) = 9

2x -39 + 6x = 9

8x - 39 = 9

8x = 9+39

8x = 48

x = 6

Since y = 13-2x

y = 13-2(6)

y = 13-12

y = 1

The soluton to the system of equation is (6, 1)

Given the equations;

99x + 101y = 499; .... 1 * 101

101x + 99 y = 501 ... 2 * 99

______________

9999x + 10,201y = 50,399

9999x + 9801y = 49,599

Subtract

10201y - 9801y = 50399-49599

400y = 800

y = 2

Substitute y = 2 into 1;

From 1;

99x + 101y = 499

99x + 101(2) =499

99x +202 = 499

99x = 499 - 202

99x = 198

x = 198/99

x =2

Hence the solution is (2,2)

For the equations;

49x - 57y = 172 .... * 57

57x - 49y = 252 __ * 49

____________________

2793x -3249y = 9804

2793x - 2401y = 12348

Subtract

-3249y+2401y = 9804-12348

-848y = -2544

y = 3

Substitute into 1;

49x - 57y = 172

49x - 57(3) = 172

49x - 171 = 172

49x = 171+172

49x = 343

x = 7

Hence the solution is (7, 3)