Question

In the xy-plane, the lines with equations 2x+2y=1 and 4x−y=4 intersect at the point with coordinates (a,b). what is the value of b ?

Answer 1

I recommend solving the second equation above for y. That will be y=4x-4. Now sub that value of y into the first equation for y and get 2x+2(4x-4)=1. Expand to get 2x + 8x - 8 = 1. Combine like terms and we get 10x = 9 and
`x= (9)/(10)`. Now we need to plug that x value into any equation we have to solve for y (your "b").
`2( (9)/(10))+2y=1` and
`(9)/(5)+2y=1`. Then
`2y= (5)/(5)- (9)/(5) = (-4)/(5)`. Multiplying both sides by 1/2 gives us that y = -2/5. That's your "b" value you're looking for.