How do you solve 4x - y = 64x−y=6 and 3x + y = 13x+y=1?

1 Answer
mason m
Feb 11, 2016

x=1,y=-2x=1,y=−2

Explanation:

Notice that when the two equations are added to one another, the yy and -y−y terms will cancel. This is opportune because we will be left with just xx terms.

Add the two equations:

{:(color(white)("(")4x,-y,=6," "),("("3x,+y,=1")",+),(color(white)("(")color(blue)(7x),cancel(+0y),color(blue)(=7)," "):}

The resulting equation 7x=7 can be divided by 7 on both sides:

(7x)/7=7/7" "" "=>" "" "color(red)(x=1

This can be substituted into either equation to solve for y. I'll choose the second equation.

3color(red)x+y=1" "" "=>" "" "3color(red)((1))+y=1

Solve the resulting equation:

3+y=1

color(green)(y=-2

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