Solve the system of equations by substitution. Your answer should be given as an ordered pair like this (x, y). Round your answers to the nearest tenth.
y=-2+7x
10x-7y=209
so, make the substitution:
10x - 7(-2+7x) = 209
10x + 14 - 49x = 209
-39x = 195
x = -5
y=-2+7(-5) = -37
To solve the system of equations by substitution, we will substitute the value of y from the first equation into the second equation and solve for x.
Given:
y = -2 + 7x ---(1)
10x - 7y = 209 ---(2)
Step 1: Substitute the value of y from equation (1) into equation (2):
10x - 7(-2 + 7x) = 209
Step 2: Simplify the expression:
10x + 14 - 49x = 209
Combine like terms:
-39x + 14 = 209
Step 3: Move the constant term to the other side of the equation:
-39x = 209 - 14
-39x = 195
Step 4: Divide both sides by -39 to solve for x:
x = 195 / -39
x = -5
Step 5: Substitute the value of x = -5 into equation (1) to find the value of y:
y = -2 + 7(-5)
y = -2 - 35
y = -37
Therefore, the solution for the system of equations is (x, y) = (-5, -37).