Solve algebraically: 2x - 5y = 11, 3x + 2y = 7
Here we have two simultaneous equations with two unknowns. In order to solve this, we must first elimate one of the variables.
To do this we will first make the coefficient (the number before) of one of the unknown variables the same in both equations.
In this question we can multiple equation 1 by 2 (this means multiplying each individual component) so that;
4x - 10y = 22
Now the coefficient of y is -10. We can make the coefficent of y 10 in equation 2 by multiplying by 5:
15x + 10y = 35
The coefficients of y are now 10 and -10. Now we can solve for x by adding both equations together:
19x = 57
Divide both sides by 19 and x = 3.
To solve for y, all we need to do is substitute x=3 back into our original equation:
2(3) - 5y = 11
6 - 5y = 11
-5y = 6
y = -1
To check the answer we can substitute both values back into the other equation:
3(3) + 2(-1) = 7 -> Which is true.
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