Final answer:
To solve the system of equations, we will solve one equation for one variable and substitute into the other equation. The solution is x = 1 and y = -7. The solution can be checked by substituting the values into both equations.
Step-by-step explanation:
To solve the system of equations using substitution, we will solve one equation for one variable and substitute that expression into the other equation.
Given:
y = 3x - 10 (1)
5x + 2y = -9 (2)
From equation (1), we can solve for y:
y = 3x - 10
Substitute this into equation (2):
5x + 2(3x - 10) = -9
Simplify and solve for x:
5x + 6x - 20 = -9
11x = 11
x = 1
Substitute x = 1 back into equation (1) to find y:
y = 3(1) - 10
y = -7
Therefore, the solution to the system of equations is x = 1 and y = -7.
To check our solution, substitute the values of x and y into both equations and see if they hold true.
For equation (1), when x = 1 and y = -7:
-7 = 3(1) - 10
-7 = -7
The equation is true.
For equation (2), when x = 1 and y = -7:
5(1) + 2(-7) = -9
-9 = -9
The equation is true.