-2x + y = 5
6x - 3y = -9
From the first equation, solve for y:
y = 2x + 5
Substitute into the second equation:
6x - 3(2x + 5) = -9
6x - 6x - 15 = -9
-15 = -9 → Contradiction
No solution.
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y = x + 4
3x - 4y = -19
Substitute y from the first equation into the second:
3x - 4(x + 4) = -19
3x - 4x - 16 = -19
-x - 16 = -19
-x = -3
x = 3
Now substitute x = 3 into y = x + 4:
y = 3 + 4 = 7
Solution: (3, 7)
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-4x + y = 6
-5x - y = 21
Solve the first equation for y:
y = 4x + 6
Substitute into the second equation:
-5x - (4x + 6) = 21
-5x - 4x - 6 = 21
-9x = 27
x = -3
Substitute x = -3 into y = 4x + 6:
y = 4(-3) + 6 = -12 + 6 = -6
Solution: (-3, -6)
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6x + 4y = -8
-6x + y = 28
Solve the second equation for y:
y = 6x + 28
Substitute into the first equation:
6x + 4(6x + 28) = -8
6x + 24x + 112 = -8
30x = -120
x = -4
Substitute x = -4 into y = 6x + 28:
y = 6(-4) + 28 = -24 + 28 = 4
Solution: (-4, 4)
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x = -2y
x - 9 = 9
Substitute x = -2y into the second equation:
-2y - 9 = 9
-2y = 18
y = -9
Substitute y = -9 into x = -2y:
x = -2(-9) = 18
Solution: (18, -9)
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x + y = 3
x - y = -3
Solve the first equation for x:
x = 3 - y
Substitute into the second equation:
(3 - y) - y = -3
3 - 2y = -3
-2y = -6
y = 3
Substitute y = 3 into x = 3 - y:
x = 3 - 3 = 0
Solution: (0, 3)
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x = y - 4
-2x + 3y = 6
Substitute x = y - 4 into the second equation:
-2(y - 4) + 3y = 6
-2y + 8 + 3y = 6
y + 8 = 6
y = -2
Substitute y = -2 into x = y - 4:
x = -2 - 4 = -6
Solution: (-6, -2)
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-5x + 20 = 5y
-2x + y = 7
Solve the second equation for y:
y = 2x + 7
Substitute into the first equation:
-5x + 20 = 5(2x + 7)
-5x + 20 = 10x + 35
-15x = 15
x = -1
Substitute x = -1 into y = 2x + 7:
y = 2(-1) + 7 = -2 + 7 = 5
Solution: (-1, 5)
Parent Tip: Review the logic above to help your child master the concept of two variable equations worksheet.
