Question

Choose the answer from the following:
Solve the given system of linear equations using the substitution method
$x=2y-1$
$x=y$

• A. $(2,2)$
• B. $(0,0)$
• C. $(1,1)$
• D. $(3,3)$

Answer 1

The correct option is C $(1,1)$

Given,
$x=2y-1\dots \left(i\right)$
$x=y\dots \left(ii\right)$
Step 1: Find the value of y
Substituting $x=y$ in $\left(i\right),$ we get
Equation $\left(i\right)$ $\to$ $\left(x\right)=2y-1$
$\left(y\right)=2y-1$
$\Rightarrow y-2y=-1\Rightarrow -y=-1\Rightarrow y=1$

Step 2: Now, Find the value of x
Substitute $y=1$ in equation $\left(i\right)$
Equation $\left(i\right)$ $\to$ $x=2\left(y\right)-1$
$x=2\left(1\right)-1$
$\Rightarrow x=2-1\Rightarrow x=1$
$\therefore x=1,y=1$

$\therefore$ Required solution for the given pair of equations is $(1,1)$