`y=(1)/(5)x+4`
`y=(3)/(7)x-4`
If the ordered pair (x, y) satisfies the system of equations above, what is the value of y?

Options

A. `0`
B. `7`
C. `10`
D. `11`

Answer

D

Explanation

Difficult: Medium
Category: Heart of Algebra/ System of Linear Equations
Strategic Advice: When both equations in a system are written in the form `y=mx+b`, use substitution or graphing to find the solutions to the system. Use whichever method gets you to the answer more quickly.
Getting to the Answer: Substitute the first expression for y into the second equation. Then clear the fractions by multiplying everything by 35 to make the numbers easier to work with , and solve for x:
`(1)/(5)x+4=(3)/(7)x-4`
`35((1)/(5)x+35(4))=35((3)/(7)x)-36(4)`
`7x+140=15x-140`
`280=8x`
x=35
The equation asks for the value of y, so substitute 35 into either of the original equation and solve for y: `y=(1)/(5)(35)+4=7+4=11` , which is (D) .