# What is the solution of y = 3x - 4 and 2x - y = 1?

Jun 4, 2018

$x = 3 , y = 5$

#### Explanation:

Rearrange to make $y$ the subject

$2 x - y = 1 \implies y = 2 x - 1$

Now you have two equations with $y =$ so equate them

$3 x - 4 = 2 x - 1$

$3 x = 2 x + 3$

Subtract $2 x$ from both sides

$x = 3$

Substitute $x = 3$ into $y = 3 x - 4 \implies y = 9 - 4 , y = 5$

Jun 4, 2018

$x = 3 \mathmr{and} y = 5$

#### Explanation:

Notice that there is a single $y$ term in each equation,

Make $y$ the subject in each case.

$\textcolor{b l u e}{y = 3 x - 4} \text{ "and" } \textcolor{red}{y = 2 x - 1}$

We know that $\text{ } \textcolor{b l u e}{y} = \textcolor{red}{y}$

$\therefore \text{ "color(blue)( 3x-4)" "=" } \textcolor{red}{2 x - 1}$

$\textcolor{w h i t e}{\times \times \times} 3 x - 2 x = - 1 + 4$

$\textcolor{w h i t e}{\times \times \times \times \times x} x = 3$

$y = 2 x - 1$

$y = 2 \left(3\right) - 1 = 5$