Answer:
(2,11)
Explanation:
What is substitution method?
The substitution method is where you plug in an expression that defines a variable into the other equation so you are left with one variable in which you can solve for.
In order to use the substitution method, one of the variables must be defined by an expression (e.g. x = 8y + 2 , the x is defined by the expression 8y + 2. )
Rearranging terms to define x or y
We have the two equations 2x + y = 15 and 7x - 2y = -8
The equation we would rearrange would likely be 2x + y = 15 as the y is by itself meaning we could easily change a few things to define it.
2x + y = 15
==> subtract 2x from both sides
2x - 2x + y = 15 - 2x
==> simplify
y = 15 - 2x
Plugging ( or substituting ) y's defined expression into the other equation.
Now that we have rearranged the equation to where "y" is being defined we can plug in the expression defined by y into the other equation and then solve for x.
2nd equation : 7x - 2y = -8
==> plug in y = 15 - 2x
7x - 2(15-2x) = -8
==> distribute the 2
7x - 30 + 4x = -8
==> combine like terms
11x - 30 = -8
==> add 30 to both sides
11x = 22
==> divide both sides by 11
x = 2
Substituing the value of x into one of the equations and then solving for y.
Now that we have calculated the value of x we can calculate the value of y by plugging in the value of x into one of the equations and solving for y.
2x + y = 15
==> plug in x = 2
2(2) + y = 15
==> multiply 2 and 2
4 + y = 15
==> subtract 4 from both sides
y = 11
The solution is (2,11)
Checking our work:
To check our work we can plug in the value of x and y into both equations. If both are true then the solution is correct but if one or both are false then the solution is incorrect.
First equation; 2x + y = 15
==> plug in x = 2 and y = 11
2(2) + 11 = 15
==> multiply 2 and 2
4 + 11 = 15
==> add 4 and 11
15 = 15
Second equation; 7x - 2y = -8
==> plug in x = 2 and y = 11
7(2) - 2(11) = -8
==> multiply 7 by 2 and 11 by -2
14 - 22 = -8
==> subtract 22 from 14
-8 = -8
Both are correct therefore (2,11) is the correct solution