Substitution Method 2

Years

Year 11

Simultaneous Equations

Substitution Method

Substitution Method 2

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Question 1 of 5

Solve the following simultaneous equations by substitution.

2 x - y = 6

$2x-y=6$

x + 3 y = 10

$x+3y=10$

$x =$ $x=$ (4)

$y =$ $y=$ (2)

Question 2 of 5

Solve the following simultaneous equations by substitution.

$2x+y=1$

$x-y=2$

$x=$ (1)

$y=$ (-1)

Question 3 of 5

Solve the following simultaneous equations by substitution.

$2x+y=7$

$4x-2y=10$

$x=$ (3)

$y=$ (1)

Question 4 of 5

Solve the following simultaneous equations by substitution.

$3x-2y=20$

$x+2y=-4$

$x=$ (4)

$y=$ (-4)

Question 5 of 5

Solve the following simultaneous equations by substitution.

$a-b=5$

$2a+b=4$

$a=$ (3)

$b=$ (-2)

$2 x - y$ $2x-y$	$=$ $=$	$6$ $6$	Equation $1$ $1$
$x + 3 y$ $x+3y$	$=$ $=$	$10$ $10$	Equation $2$ $2$

$2 x - y$ $2x-y$	$=$ $=$	$6$ $6$
$2 x - y$ $2x-y$ $+ y - 6$ $+y-6$	$=$ $=$	$6$ $6$ $+ y - 6$ $+y-6$	Add $y - 6$ $y-6$ to both sides
$2 x - 6$ $2x-6$	$=$ $=$	$y$ $y$	Simplify
$y$ $y$	$=$ $=$	$2 x - 6$ $2x-6$	Simplify

$x + 3$ $x+3$ $y$ $y$	$=$ $=$	$10$ $10$	Equation $2$ $2$
$x + 3$ $x+3$ $(2 x - 6)$ $(2x-6)$	$=$ $=$	$10$ $10$	$y = 2 x - 6$ $y=2x-6$
$x + 6 x - 18$ $x+6x-18$	$=$ $=$	$10$ $10$	Distribute $3$ $3$ inside the parenthesis
$7 x - 18$ $7x-18$	$=$ $=$	$10$ $10$	Simplify
$7 x - 18$ $7x-18$ $+ 18$ $+18$	$=$ $=$	$10$ $10$ $+ 18$ $+18$	Solve for $x$ $x$
$7 x$ $7x$	$=$	$28$
$x$	$=$	$4$	Divide both sides by $7$

$2$ $x$ $-y$	$=$	$6$	Equation $1$
$2$ $(4)$ $-y$	$=$	$6$	$x=4$
$8-y$	$=$	$6$
$8-y$ $-8$	$=$	$6$ $-8$	Simplify
$-y$	$=$	$-2$
$y$	$=$	$2$

$2x+y$	$=$	$1$	Equation $1$
$x-y$	$=$	$2$	Equation $2$

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Quiz summary

Information

1. Question

Hint

Correct!

2. Question

Hint

Fantastic!

3. Question

Hint

Correct!

Substitution Method

4. Question

Hint

Fantastic!

Substitution Method

5. Question

Hint

Nice Job!

Substitution Method

Quizzes

$x-y$	$=$	$2$
$x-y$ $+y$	$=$	$2$ $+y$	Add $y$ to both sides of the equation
$x$	$=$	$2+y$	Simplify

$2$ $x$ $+y$	$=$	$1$	Equation $1$
$2$ $(2+y)$ $+y$	$=$	$1$	$x=2+y$
$4+2y+y$	$=$	$1$	Distribute $2$ inside the parenthesis
$4+3y$	$=$	$1$	Simplify
$4+3y$ $-4$	$=$	$1$ $-4$	Solve for $y$
$3y$	$=$	$-3$
$y$	$=$	$-1$	Divide both sides by $3$

$x-$ $y$	$=$	$2$	Equation $2$
$x-$ $(-1)$	$=$	$2$	$y=-1$
$x+1$	$=$	$2$
$x+1$ $-1$	$=$	$2$ $-1$	Simplify
$x$	$=$	$1$

$2x+y$	$=$	$7$
$2x+y$ $-2x$	$=$	$7$ $-2x$	Subtract $2x$ from both sides
$y$	$=$	$7-2x$	Simplify

$4x-2$ $y$	$=$	$10$	Equation $2$
$4x-2$ $(7-2x)$	$=$	$11$	$y=7-2x$
$4x-14+4x$	$=$	$10$	Distribute $2$ inside the parenthesis
$8x-14$	$=$	$10$	Simplify
$8x-14$ $+14$	$=$	$10$ $+14$	Solve for $x$
$8x$	$=$	$24$
$8x$ $div8$	$=$	$24$ $div8$	Divide both sides by $8$
$x$	$=$	$3$

$2$ $x$ $+y$	$=$	$7$	Equation $1$
$2$ $(3)$ $+y$	$=$	$7$	$x=3$
$6+y$ $-6$	$=$	$7$ $-6$	Subtract $6$ from both sides
$y$	$=$	$1$

$2x+y$	$=$	$7$
$2(3)+1$	$=$	$7$	Substitute $x=3$ and $y=1$
$6+1$	$=$	$7$
$7$	$=$	$7$

$x+2y$	$=$	$-4$
$x+2y$ $-2y$	$=$	$-4$ $-2y$	Subtract $2y$ from both sides
$x$	$=$	$-4-2y$	Simplify

$3$ $x$ $-2y$	$=$	$20$	Equation $1$
$3$ $(-4-2y)$ $-2y$	$=$	$20$	$x=-4-2y$
$-12-6y-2y$	$=$	$20$	Distribute $3$ inside the parenthesis
$-12-8y$	$=$	$20$	Simplify
$-12-8y$ $+12$	$=$	$20$ $+12$	Solve for $y$
$-8y$	$=$	$32$
$-8y$ $div(-8)$	$=$	$32$ $div(-8)$	Divide both sides by $-8$
$y$	$=$	$-4$

$x+2$ $y$	$=$	$-4$	Equation $2$
$x+2$ $(-2)$	$=$	$-4$	$y=-2$
$x-8$ $+8$	$=$	$-4$ $+8$	Add $8$ to both sides
$x$	$=$	$4$

$a-b$	$=$	$5$
$a-b$ $+b$	$=$	$5$ $+b$	Add $b$ to both sides
$a$	$=$	$5+b$	Simplify

$2$ $a$ $+b$	$=$	$4$	Equation $2$
$2$ $(5+b)$ $+b$	$=$	$4$	$a=5+b$
$10+2b+b$	$=$	$4$	Distribute $2$ inside the parenthesis
$10+3b$	$=$	$4$	Simplify
$10+3b$ $-10$	$=$	$4$ $-10$	Solve for $b$
$3b$	$=$	$-6$
$3b$ $div3$	$=$	$-6$ $div3$	Divide both sides by $3$
$b$	$=$	$-2$

$a-$ $b$	$=$	$5$	Equation $1$
$a-$ $(-2)$	$=$	$5$	$b=2$
$a+2$	$=$	$5$	Simplify
$a+2$ $-2$	$=$	$5$ $-2$	Subtract $2$ from both sides
$a$	$=$	$3$