Question

Solve the system by either substitution or elimination.%0D%0A%0D%0A3x−5y=212x+y=1(1 point)%0D%0AResponses%0D%0A%0D%0A(2,−3)%0D%0A(%0D%0A2%0D%0A,%0D%0A−%0D%0A3%0D%0A)%0D%0Aopen paren 2 comma negative 3 close paren%0D%0A%0D%0A(2,3)%0D%0A(%0D%0A2%0D%0A,%0D%0A3%0D%0A)%0D%0Aopen paren 2 comma 3 close paren%0D%0A%0D%0A(−2,−1)%0D%0A(%0D%0A−%0D%0A2%0D%0A,%0D%0A−%0D%0A1%0D%0A)%0D%0Aopen paren negative 2 comma negative 1 close paren%0D%0A%0D%0A(−2,1)

Answer 1

To solve the system by substitution, we can solve one of the equations for one variable and then substitute that expression into the second equation.

Let's solve the second equation for y:

2x + y = 1
y = 1 - 2x

Now, substitute this expression for y into the first equation:

3x - 5(1 - 2x) = 21
3x - 5 + 10x = 21
13x - 5 = 21
13x = 26
x = 2

Now substitute the value of x back into the second equation to find y:

2(2) + y = 1
4 + y = 1
y = -3

Therefore, the solution to the system of equations is (2, -3).