Answer
$$x=4$$ $$y=-5$$
Work Step by Step
Equation 1: $3x + y = 7$
Equation 2: $4x + 3y = 1$
Multiply equation 1 by $-3$:
$$[3x + y = 7]\cdot-3$$ $$-9x -3y =-21$$
Add this equation to equation 2:
$$-9x -3y =-21$$ $$+$$ $$4x + 3y = 1$$ $$=$$ $$-5x=-20$$
Divide both sides by $-5$:
$$\frac{-5x}{-5}=\frac{-20}{-5}$$ $$x=4$$
Substitute this value of $x$ to equation 1:
$$3x + y = 7$$ $$3(4) + y = 7$$ $$12 + y = 7$$
Subtract $12$ from both sides:
$$12 -12+ y = 7-12$$ $$y=-5$$
Use equation 2 to check:
$$4x + 3y = 1$$ $$4(4) + 3(-5) = 1$$ $$16 -15 = 1$$ $$1=1$$
