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4.02 Substitution method

Adaptive
Worksheet

Interactive practice questions

Consider the system of equations:

$y=x-8$y=x8

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

Which of the following points satisfies the system?

$\left(3,-5\right),\left(4,-4\right),\left(6,-2\right)$(3,5),(4,4),(6,2)

$\left(3,-5\right)$(3,5)

A

$\left(6,-2\right)$(6,2)

B

$\left(4,-4\right)$(4,4)

C
Easy
1min

Which ordered pair is a solution to the following system of equations?

$y$y $=$= $5x$5x $-$ $4$4
$y$y $=$= $-x$x $+$+ $20$20
Easy
< 1min

Does there exist a value for $x$x and $y$y that satisfy the following two equations simultaneously?

$y=-4x+4$y=4x+4

$y=-8x+4$y=8x+4

Medium
< 1min

Consider the point of intersection where the vertical line $x=8$x=8 meets the line $y=4x+8$y=4x+8.

Medium
1min
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Outcomes

A.EI.2

The student will represent, solve, explain, and interpret the solution to a system of two linear equations, a linear inequality in two variables, or a system of two linear inequalities in two variables.

A.EI.2a

Create a system of two linear equations in two variables to represent a contextual situation.

A.EI.2b

Apply the properties of real numbers and/or properties of equality to solve a system of two linear equations in two variables, algebraically and graphically.

A.EI.2c

Determine whether a system of two linear equations has one solution, no solution, or an infinite number of solutions.

A.EI.2h

Verify possible solution(s) to a system of two linear equations, a linear inequality in two variable, or a system of two linear inequalities algebraically, graphically, and with technology to justify the reasonableness of the answer(s). Explain the solution method and interpret solutions for problems given in context.

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