Solve the following system using the substitution method:
3x + y = -3
y = 2x + 7
we see that y = -3x-3
substitute that into the other euation to get
-3x-3 = 2x+7
-5x = 10
x = -2
so, y = -3(-2)-3 = 3
check to make sure (-2,3) solves both equations.
3x+y=3
Y=2x-7
To solve the system of equations using the substitution method, we need to substitute one equation into the other to find the value(s) of the variables.
In this case, we have two equations:
1) 3x + y = -3
2) y = 2x + 7
Let's solve equation 2) for y and substitute this value into equation 1):
Substitute y = 2x + 7 into equation 1):
3x + (2x + 7) = -3
Now simplify the equation:
3x + 2x + 7 = -3
5x + 7 = -3
Next, isolate the x variable by subtracting 7 from both sides:
5x = -3 - 7
5x = -10
Now divide both sides by 5 to solve for x:
x = -10 / 5
x = -2
Now that we know the value of x, substitute it back into equation 2) to find the value of y:
y = 2(-2) + 7
y = -4 + 7
y = 3
Therefore, the solution to the system of equations is:
x = -2
y = 3
3x + y = -3
y = 2x + 7
3x + 2x + 7 = -3
5x = -10
x = -2
y - (2 * -2) + 7
y = 7 - 4
y = 3