a In each system of equations, isolate one of the variables in one of the equations. Then solve by substitution.
B
b In each system of equations, isolate one of the variables in one of the equations. Then solve by substitution.
C
c In each system of equations, isolate one of the variables in one of the equations. Then solve by substitution.
D
d In each system of equations, isolate one of the variables in one of the equations. Then solve by substitution.
E
e In each system of equations, isolate one of the variables in one of the equations. Then solve by substitution.
F
f In each system of equations, isolate one of the variables in one of the equations. Then solve by substitution.
A
a We solve the first equation for x, as it has the coefficient 1. (-5,-1).
B
b We solve the first equation for x, as it has the coefficient 1. (-2,2).
C
c We solve the second equation for y, as it has the coefficient 1. (2,-2).
D
d We solve the second equation for x, as it has the coefficient 1. (3,2).
E
e We solve the second equation for x by changing the signs. (1,-3).
F
f We solve the first equation for y by changing the signs. (-1,3).
Practice makes perfect
a In the first equation, the coefficient for x is 1. We only need to subtract 2y from the equation to isolate it. Then we can substitute the expression into the second equation.
Hence, the solution to this system of equations is:
x=-5 y=-1.
Now, let's substitute the ordered pair (-5,-1) into both equations, to check whether our solution is correct.
x+2y=-7 & (I) 2x-y=-9 & (II)
(I), (II): x= -5, y= -1
-5+2( -1)? =-7 2( -5)-( -1)? =-9
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(I), (II): Evaluate equations
(I), (II): Multiply
-5-2? =-7 -10+1? =-9
(I), (II): Add and subtract terms
-7=-7 -9=-9
Both equations are satisfied with this ordered pair, so our solution is correct.
b In the first equation, the coefficient for x is 1. We only need to add 2y to the equation to isolate it. Then we can substitute the expression into the second equation.
Hence, the solution to this system of equations is
x=-2 y=2.
Now, let's substitute the ordered pair (-2,2) into both equations, to check whether our solution is correct.
x-2y=-6 & (I) 2x+y=-2 & (II)
(I), (II): x= -2, y= 2
-2-2* 2? =-6 2( -2)+ 2? =-2
(I), (II): Multiply
-2-4? =-6 -4+2? =-2
(I), (II): Add and subtract terms
-6=-6 -2=-2
Both equations are satisfied with this ordered pair, so our solution is correct.
c In the second equation, the coefficient for y is 1. We only need to add 2x to the equation to isolate it. Then we can substitute the expression into the first equation.
Hence, the solution to this system of equations is
x=2 y=-2.
Now, let's substitute the ordered pair (2,-2) into both equations, to check whether our solution is correct.
-3x+2y=-10 & (I) -2x+y=-6 & (II)
(I), (II): x= 2, y= -2
-3* 2+2( -2)? =-10 -2* 2+( -2)? =-6
(I), (II): Multiply
-6-4? =-10 -4-2? =-6
(I), (II): Subtract terms
-10=-10 -6=-6
Both equations are satisfied with this ordered pair, so our solution is correct.
d In the second equation, the coefficient of x is 1. We only need to add 3y to the equation to isolate it. Then we can substitute the expression into the first equation.
Hence, the solution to this system of equations is
x=3 y=2.
Now, let's substitute the ordered pair (3,2) into both equations, to check whether our solution is correct.
3x+2y=13 & (I) x-3y=-3 & (II)
(I), (II): x= 3, y= 2
3* 3+2* 2? =13 3-3* 2? =-3
(I), (II): Multiply
9+4? =13 3-6? =-3
(I), (II): Add and subtract terms
13=13 -3=-3
Both equations are satisfied with this ordered pair, so our solution is correct.
e The coefficient of x in the second equation is -1. We can isolate it by changing the signs of the entire equation first. Then we can substitute it into the first equation.
Hence, the solution to this system of equations is
x=1 y=-3.
Now, let's substitute the ordered pair (1,-3) into both equations, to check whether our solution is correct.
3x-2y=9 & (I) - x-3y=8 & (II)
(I), (II): x= 1, y= -3
3* 1-2( -3)? =9 - 1-3( -3)? =8
(I), (II): Multiply
3+6? =9 -1+9? =8
(I), (II): Add terms
9=9 8=8
Both equations are satisfied with this ordered pair, so our solution is correct.
f The coefficient of y in the first equation is -1. We can isolate it by changing the signs of the entire equation first. Then we can substitute it into the second equation.
Hence, the solution to this system of equations is
x=-1 y=3.
Now, let's substitute the ordered pair (-1,3) into both equations, to check whether our solution is correct.
3x-y=-6 & (I) 4x+5y=11 & (II)
(I), (II): x= -1, y= 3
3( -1)- 3? =-6 4( -1)+5* 3? =11
(I), (II): Multiply
-3-3? =-6 -4+15? =11
(I), (II): Add and subtract terms
-6=-6 11=11
Both equations are satisfied with this ordered pair, so our solution is correct.
