Solve the following system of equations. Find the x-coordinate of the solution. Round your answer to the nearest tenth.
5x + 2y = 22
-2x + 6y = 3
- 5x + 2y = 22, 2. -2x +6y = 3
A. the first thing I want to do is to isolate the 2y because there is a multiple of is in equation#2, 6y
1.> 5x + 2y = 22 >> 3. 2y = 22 - 5x, now multiplying both sides by 3 we get: 6y = 66 - 15x
B. plug 6y back into equation 2.
2.[-2x + 6y = 3]… -2x + (6y) = -2x + 66 - 15x = 3
C. now that you have a single variable equation, a true statement with only the x variable(this is the goal here) we can solve for x.
-2x + 66 - 15x =(combining terms) -17x + 66 = 3 --(subtract 66 from both sides)>> -17x = -63 —(divide by negative 17 and…)–>>
x = (-63/-17) =
63/17 = 3.7059 or 3.7 rounded to the nearest tenth.
(extra)D. Now that we know the value of x(=63/17 or 3.7) we can plug it back into which ever equation we’d like to find the value of y
- -2x + 6y = 3, subbing or found value for x we get : -2(3.7) + 6y = 3 --(multiply it out and move constants(non-variable terms) to the other side)–>> 6y = 10.4
thus, y = (10.4/6 = 1.7)
the coordinate solution of this system of equations is x=3.7 and y = 10.4 (3.7,10.4)