How do I solve 3x + y = 11 & 2x + y = 8?
In order to solve this set of simultaneous equations, we will rearrange each equation to use substitution. The aim of this problem is to find out what the value of x and y is. Let's rearrange equation 1 and make y the subject of the equation (i.e. move y to the left of the equals sign, and everything else to the right).
3x + y = 11
y = 11 - 3x
We have rearranged equation 1 so we now have an expression for y in terms of x. Let's now substitute this value of y into equation 2.
2x + y = 8
2x + (11 - 3x) = 8
We now have an equation in terms of x only, so we can go ahead and solve for x.
2x -3x = 8-11
-x = -3
x = 3
We have now obtained a value for x. Now, to find out what y is we just need to substitute it back into our equation for y.
y = 11 -3x
y = 11- 3*3
y = 11-9
y = 2
In a simultaneous equation, you can always double check your answer is correct by substituting your values of x and y into any of the equations and seeing if it holds true. Lets test this by substituting x = 3 and y = 2 into equation 2.
2x + y = 8
2*3 + 2 = 6 + 2 = 8
As these values satisfy the equation, we know that our answer is correct.
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