Question

Describe and correct the error in solving the system of linear equations : the solution of the linear equation y=0.5x+1 and y=-x+7 is x=4

Answer 1

To solve this system of equations we can use the substitution method. Substitute what 'y' equals in the first equation into the second:

$\sf y=0.5x+1$
$\sf y=-x+7$

$\sf 0.5x+1=-x+7$

Now solve for 'x', subtract 1 to both sides:

$\sf 0.5x=-x+6$

Add 'x' to both sides:

$\sf 1.5x=6$

Divide 1.5 to both sides:

$\sf x=4$

So the x-value of the solution to this system is 4, now plug this into any of the two equations to find the y-value:

$\sf y=0.5x+1$

$\sf y=0.5(4)+1$

$\sf y=2+1$

$\sf y=3$

This is the y-value of our solution, so the entire solution to this system of equations is (4, 3).