Solve using elimination.
10x + y = -19
6x − 2y = -14
Multiply first equation by 2. Add the two equations to find x. Then insert that value into either equation to find y.
To solve the system of equations using the elimination method, we need to eliminate one of the variables. In this case, let's eliminate the y variable.
First, we'll multiply both sides of the second equation by 1/2 to make the coefficient of y the same for both equations:
(1/2)(6x − 2y) = (1/2)(-14)
3x - y = -7
Now, we can proceed to eliminate the y variable by adding the two equations together:
(10x + y) + (3x - y) = -19 + (-7)
10x + 3x + y - y = -26
13x = -26
To isolate x, we divide both sides of the equation by 13:
13x/13 = -26/13
x = -2
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
10(-2) + y = -19
-20 + y = -19
y = -19 + 20
y = 1
Therefore, the solution to the system of equations is x = -2 and y = 1.