Here are the solutions for each problem on the worksheet using the substitution method.
1)
Substitute $y = -7x$ into the second equation:
$$-7x = -x - 4$$
Add $x$ to both sides:
$$-6x = -4$$
Divide by $-6$:
$$x = \frac{-4}{-6} = \frac{2}{3}$$
Find $y$:
$$y = -7\left(\frac{2}{3}\right) = -\frac{14}{3}$$
2)
Since $y = -4$, substitute this into the second equation:
$$-4 = -2x - 2$$
Add $2$ to both sides:
$$-2 = -2x$$
Divide by $-2$:
$$x = 1$$
3)
Substitute $y = -6$ into the first equation:
$$-6 = 3x - 12$$
Add $12$ to both sides:
$$6 = 3x$$
Divide by $3$:
$$x = 2$$
4)
Substitute $y = 8$ into the second equation:
$$8 = x + 8$$
Subtract $8$ from both sides:
$$x = 0$$
5)
Substitute $y = 3$ into the second equation:
$$3 = -3x - 21$$
Add $21$ to both sides:
$$24 = -3x$$
Divide by $-3$:
$$x = -8$$
6)
Substitute $y = -6$ into the second equation:
$$-6 = -7x - 6$$
Add $6$ to both sides:
$$0 = -7x$$
Divide by $-7$:
$$x = 0$$
7)
Substitute $y = -8$ into the first equation:
$$-8 = -8x - 8$$
Add $8$ to both sides:
$$0 = -8x$$
Divide by $-8$:
$$x = 0$$
8)
Substitute $y = 3$ into the second equation:
$$3 = x - 2$$
Add $2$ to both sides:
$$x = 5$$
9)
Substitute $y = -3$ into the first equation:
$$-3 = 2x - 1$$
Add $1$ to both sides:
$$-2 = 2x$$
Divide by $2$:
$$x = -1$$
10)
Substitute $y = -2$ into the first equation:
$$-2 = 3x - 23$$
Add $23$ to both sides:
$$21 = 3x$$
Divide by $3$:
$$x = 7$$
11)
Set the equations equal to each other since they both equal $y$:
$$-6x = -7x - 6$$
Add $7x$ to both sides:
$$x = -6$$
Find $y$:
$$y = -6(-6) = 36$$
12)
Set the equations equal to each other:
$$-4x = -5x - 5$$
Add $5x$ to both sides:
$$x = -5$$
Find $y$:
$$y = -4(-5) = 20$$
Final Answer:
1) $x = 2/3, y = -14/3$
2) $x = 1, y = -4$
3) $x = 2, y = -6$
4) $x = 0, y = 8$
5) $x = -8, y = 3$
6) $x = 0, y = -6$
7) $x = 0, y = -8$
8) $x = 5, y = 3$
9) $x = -1, y = -3$
10) $x = 7, y = -2$
11) $x = -6, y = 36$
12) $x = -5, y = 20$
Parent Tip: Review the logic above to help your child master the concept of solve equations for y worksheet.
