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7.03 Solving systems of equations with the elimination method

Interactive practice questions

Consider the following system of equations.

Equation 1 $3x+7y=-6$3x+7y=6
Equation 2 $2x-y=-17$2xy=17

Suppose we want to solve this system by using the elimination method and eliminating $y$y.

a

What value can we multiply Equation 2 by so that the coefficients of $y$y in each equation are opposite numbers?

b

What equation do we get when we multiply the second equation by $7$7?

Easy
1min

Consider this system of equations.

Equation 1 $\frac{2x}{5}+\frac{3y}{5}=-\frac{7}{5}$2x5+3y5=75
Equation 2

$-\frac{1}{4}\left(-5x+\frac{7y}{9}\right)=2$14(5x+7y9)=2

Easy
< 1min

Consider the following system of equations.

$-8x$8x $-$ $y$y $=$= $0$0
$-5x$5x $+$+ $3y$3y $=$= $6$6

We are solving this system using the elimination method.

Easy
2min

When we solve a system of equation using the addition method, what happens when the system has no solutions?

Easy
< 1min
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Outcomes

I.A.REI.5

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

I.A.REI.6

Solve systems of linear equations exactly and approximately (numerically, algebraically, graphically), focusing on pairs of linear equations in two variables.

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