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in the solution to using substitution method to solve this simultaneous equation

y-1/4x=3
and
3y+x=23

from

y-1/4x=3 we get y = 1/4 x + 3
sub that into the other equation
3(1/4 x + 3) + x = 23
(3/4)x + 9 + x = 23
(7/4)x = 14
x = 14(4/7) = 8
then y = (1/4)(8) + 3 = 5

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The substitution method is a useful technique for solving simultaneous equations. In this method, we can isolate one variable in one equation and substitute it into the other equation to solve for the remaining variable. For example, in the system of equations: y - (1/4)x = 3 3y + x = 23 We can isolate y in the first equation by adding (1/4)x to both sides, yielding y = (1/4)x + 3. Then, we substitute this expression for y into the second equation, giving us 3((1/4)x + 3) + x = 23. By simplifying this equation, we can solve for x, and then substitute this value back into the expression for y to find the solution to the system of equations. Through the power of substitution, we can unravel the mystery behind these equations and discover their solutions.