Answer
$a)$ $x$-intercepts: $\pm5;$ $y$-intercepts: $\pm2$
$b)$ $x$-intercepts: $\pm1;$ $y$-intercept: $\dfrac{1}{3}$
Work Step by Step
$a)$ $4x^{2}+25y^{2}=100$
To find the $x$-intercepts, set $y$ equal to $0$ and solve for $x$:
$4x^{2}+25y^{2}=100$
$4x^{2}+25(0)^{2}=100$
$4x^{2}=100$
$x^{2}=\dfrac{100}{4}$
$x^{2}=25$
$x=\pm\sqrt{25}$
$x=\pm5$
To find the $y$-intercepts, set $x$ equal to $0$ and solve for $y$:
$4x^{2}+25y^{2}=100$
$4(0)^{2}+25y^{2}=100$
$25y^{2}=100$
$y^{2}=\dfrac{100}{25}$
$y^{2}=4$
$y=\pm\sqrt{4}$
$y=\pm2$
$b)$ $x^{2}-xy+3y=1$
To find the $x$-intercepts, set $y$ equal to $0$ and solve for $x$:
$x^{2}-xy+3y=1$
$x^{2}-x(0)+3(0)=1$
$x^{2}=1$
$x=\pm\sqrt{1}$
$x=\pm1$
To find the $y$-intercept, set $x$ equal to $0$ and solve for $y$:
$x^{2}-xy+3y=1$
$(0)^{2}-(0)y+3y=1$
$3y=1$
$y=\dfrac{1}{3}$
