A)
5x+y=13
−x+2y=−7
Multiply each term in the first equation by -2:
5x + y = 13 x -2 = -10x - 2y = -26
Now add that to the second equation:
-10x - 2y = -26 + −x+2y=−7
= -11x = -33
Divide each side by -11
X = -33 / -11
X = 3
Now you have x, replace it in the first equation and solve for y:
5(3) + y = 13
Simplify:
15 + y = 13
Subtract 15 from both sides:
y = 13 -15
y = -2
Solution = (3,-2)
B)
4x+5y=35
−3x+2y=−9
Multiply each term in the second equation by -2.5:
7.5x -5y = 22.5
Add this to the first equation:
4x+5y=35 + 7.5x -5y = 22.5
= 11.5x = 57.5
Divide both sides by 11.5:
x = 57.5 / 11.5
x = 5
Now you have x, replace x in one of the equations to solve for y:
4(5) + 5y = 35
Simplify:
20 + 5y = 35
Subtract 20 from both sides:
5y = 15
Divide both sides by 5:
y = 15/5
y = 3
Solution = (5,3)