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Exercises about graphically solving systems of equations

Solving systems of equations graphically means reading off intersection points from a diagram.

Determining intersection points

Consider two straight lines g and h.

Determine the linear equations of g and h.

$𝗒 = 𝗆 𝗑 + 𝗍$
The parameter $𝗆$ is the slope of the straight line. The parameter $𝗍$ is the y-axis intercept.
Line g:
$𝗒 = 𝗆_{𝗀} 𝗑 + 𝗍_{𝗀}$
The straight line g has slope $- \frac{𝟥}{𝟤}$ , that is $𝗆_{𝗀} = - \frac{𝟥}{𝟤}$ .
$𝗒 = - \frac{𝟥}{𝟤} 𝗑 + 𝗍_{𝗀}$ .
It intersects the y-axis at $\frac{𝟫}{𝟤}$ , that is $𝗍_{𝗀} = \frac{𝟫}{𝟤}$ .
$𝗒 = - \frac{𝟥}{𝟤} 𝗑 + \frac{𝟫}{𝟤}$ .
Line h:
$𝗒 = 𝗆_{𝗁} 𝗑 + 𝗍_{𝗁}$
The straight line h has the slope $𝟤$ , that is $𝗆_{𝗁} = 𝟤$
$𝗒 = 𝟤 𝗑 + 𝗍_{𝗁}$
The straight line intersects the y-axis at $𝟣$ , that is $𝗍_{𝗁} = 𝟣$ .
$𝗒 = 𝟤 𝗑 + 𝟣$

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