Solve using elimination and express answer as ordered pair:
2x + 3y = 7
x + 5y = 7
I will be happy to check your work.
keep the first as is:
2x + 3y = 7
double the 2nd:
2x + 10y = 14
subtract them:
7y = 7
y = 1
sub back into the 2nd, and find x
To solve the system of equations using elimination, we need to eliminate one of the variables by multiplying one or both of the equations by suitable numbers so that the coefficients of one of the variables in both equations become the same or additive inverses of each other. Let's use the second equation and multiply it by -2 to make the x-coefficient in the equations the same but with opposite signs.
Original equations:
1) 2x + 3y = 7
2) x + 5y = 7
Multiply equation 2 by -2:
-2(x + 5y) = -2(7)
-2x - 10y = -14
Now, we can add equation 1 and the newly obtained equation:
(2x + 3y) + (-2x - 10y) = 7 + (-14)
2x - 2x + 3y - 10y = 7 - 14
-7y = -7
Divide both sides of the equation by -7 to solve for y:
y = 1
Now, substitute the value of y back into equation 2, and solve for x:
x + 5(1) = 7
x + 5 = 7
x = 7 - 5
x = 2
Therefore, the solution is x = 2 and y = 1. As an ordered pair, the solution can be expressed as (2, 1).