Solve the simultaneous equations 4x + 7y = 1 and 3x +10y = 15.

There are two main ways of solving this equation, substitution and elimination, here we go through the susbtitution method. This involves rearranging one of the equations to get one of the variables in terms of the other, for example x in terms of y. We then substitute this new expression for x into the other equation and rearrange to solve for y. We then use the value of y in either equation to solve for x.

Rearrange the first equation for x:

4x = 1 - 7y

x = (1-7y)/4

Subsitute x into the second equation:

3*((1-7y)/4) + 10y = 15

Expand the brackets:

(3/4)*(1-7y) + 10y = 15

3/4 -21y/4 + 10y = 15

Collect like terms (write 10y as 40y/4 and 15 as 60/4):

40y/4 - 21y/4 = 60/4 - 3/4

19y/4 = 57/4

Multiply by 4:

19y = 57

Rearrange for y:

y = 57/19 = 3

Subsitute y = 3 into either equation, we use the second:

3x +10*3 = 15

3x + 30 = 15

3x = 15 - 30

3x = -15

x = -15/3 = -5

Finally write the answers out:

x = -5 and y = 3.