NZ Level 6 (NZC) Level 1 (NCEA)
the Substitution Method

## Interactive practice questions

Consider this system of equations.

 Equation 1 $\frac{4x}{5}+\frac{3y}{5}=4$4x5​+3y5​=4 Equation 2 $8x-3y=5$8x−3y=5

Which operation will change the fractional coefficients to integer coefficients in this system of equations?

Multiply Equation 2 by $5$5.

A

Multiply Equation 1 by $5$5.

B

Divide Equation 2 by $3$3.

C

Divide Equation 1 by $3$3.

D

Multiply Equation 2 by $5$5.

A

Multiply Equation 1 by $5$5.

B

Divide Equation 2 by $3$3.

C

Divide Equation 1 by $3$3.

D
Easy
Less than a minute

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

Consider the following equations.

 Equation 1 $4x+7y=-9$4x+7y=−9 Equation 2 $12x+21y=-18$12x+21y=−18

We want to solve the following system of equations using the substitution method.

 Equation 1 $y=5x+34$y=5x+34 Equation 2 $y=3x+18$y=3x+18

### Outcomes

#### NA6-5

Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns

#### 91027

Apply algebraic procedures in solving problems