Question

PRACTICE SE Solve the following simultaneous equations. 7x + 4y = 26 3x-4y=-6 (b​

Answer 1

x = 2

y = 3

Explanation:

To solve a regular simultaneous equation, you need both of the equations to have the same coefficient (number) in front of the variable (x or y). In this case, the equations already have the same number in front of the y (4).

7x + 4y = 26

3x - 4y = - 6

the next step is to make one of the matching coefficients positive and one negative so they subtract to = 0, but this has already been done too.

Now we solve each part vertically, starting with the x values:

7x + 4y = 26

3x - 4y = - 6

7x + 3x = 10x

then the y values:

7x + 4y = 26

3x - 4y = - 6

4y - 4y = 0

and the values they equal:

7x + 4y = 26

3x - 4y = - 6

26 - 6 = 20

now combine these answers into an equation

10x + 0 = 20

rearrange to solve for x and simplify the fraction

x = 20/10 (let me know if you need more detail for this)

therefore x = 2

substitute x back into either of the original equations given in the question. To make it easier, i will just use the one with all positive numbers:

7x + 4y = 26

let x = 2

7(2) + 4y = 26

14 + 4y = 26

and rearrange to solve for y (again, let me know if you need more steps):

4y = 26 - 14

y = 12 / 4

y = 3

therefore x = 2 and y = 3

Answer 2

`7x+4y=26............(1)\\3x-4y=-6.............(2)\\\mathrm{Adding\ equations(1)\ and\ (2),}\\10x=20\\\mathrm{or,\ }x=2\\\mathrm{Putting\ }x\mathrm{=2\ in\ equation (2),}\\3(2)-4y=-6\\\mathrm{or,\ }6-4y=-6\\\mathrm{or,\ }-4y=-12\\\mathrm{or,\ }y=3`

`\therefore\ x=2\ \mathrm{and\ }y=3`