y9. Algebra. Changing Subject of Formula - Maths with David - Free Printable

Here are the solutions for making the specified variable the subject of each formula.

Question 1: Make y the subject

To make $y$ the subject, we need to isolate $y$ on one side of the equals sign. We do this by performing the opposite operation on both sides.

(a) $y + w = c$
Subtract $w$ from both sides:
$y = c - w$

(b) $y - p = m$
Add $p$ to both sides:
$y = m + p$

(c) $m + y = s$
Subtract $m$ from both sides:
$y = s - m$

(d) $y - 2g = n$
Add $2g$ to both sides:
$y = n + 2g$

(e) $3y = c$
Divide both sides by 3:
$y = \frac{c}{3}$

(f) $ay = w$
Divide both sides by $a$:
$y = \frac{w}{a}$

(g) $\frac{y}{c} = w$
Multiply both sides by $c$:
$y = cw$

(h) $\frac{y}{a} = 2c$
Multiply both sides by $a$:
$y = 2ac$

(i) $a = y + p$
Subtract $p$ from both sides (or swap sides first):
$y = a - p$

(j) $c = y - k$
Add $k$ to both sides:
$y = c + k$

(k) $y^2 = s$
Take the square root of both sides:
$y = \sqrt{s}$

(l) $y^3 = x$
Take the cube root of both sides:
$y = \sqrt[3]{x}$

(m) $\sqrt{y} = g$
Square both sides:
$y = g^2$

(n) $\pi y = c$
Divide both sides by $\pi$:
$y = \frac{c}{\pi}$

(o) $n - y = t$
Add $y$ to both sides and subtract $t$ from both sides:
$y = n - t$

(p) $ry = c$
Divide both sides by $r$:
$y = \frac{c}{r}$

(q) $4\pi y = b$
Divide both sides by $4\pi$:
$y = \frac{b}{4\pi}$

(r) $y + 7t = c + r$
Subtract $7t$ from both sides:
$y = c + r - 7t$

(s) $\frac{r}{y} = w$
Multiply by $y$, then divide by $w$:
$y = \frac{r}{w}$

(t) $y^2 = k + x$
Take the square root of the entire right side:
$y = \sqrt{k + x}$

(u) $A = xy$
Divide both sides by $x$:
$y = \frac{A}{x}$

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Question 2: Make x the subject

To make $x$ the subject, we isolate $x$ using inverse operations.

(a) $4x + c = w$
Subtract $c$, then divide by 4:
$x = \frac{w - c}{4}$

(b) $dx - t = 8$
Add $t$, then divide by $d$:
$x = \frac{8 + t}{d}$

(c) $x^2 + 3 = h$
Subtract 3, then take the square root:
$x = \sqrt{h - 3}$

(d) $2x + 2y = P$
Subtract $2y$, then divide by 2:
$x = \frac{P - 2y}{2}$ (or $x = \frac{P}{2} - y$)

(e) $s = x^2 - 3$
Add 3, then take the square root:
$x = \sqrt{s + 3}$

(f) $y = xz + s$
Subtract $s$, then divide by $z$:
$x = \frac{y - s}{z}$

(g) $\frac{x}{n} + 2 = w$
Subtract 2, then multiply by $n$:
$x = n(w - 2)$

(h) $\frac{x}{6} - 5 = w$
Add 5, then multiply by 6:
$x = 6(w + 5)$

(i) $\frac{x + 3}{c} = h$
Multiply by $c$, then subtract 3:
$x = ch - 3$

(j) $3y = 4x + 1$
Subtract 1, then divide by 4:
$x = \frac{3y - 1}{4}$

(k) $x^2 + a = v$
Subtract $a$, then take the square root:
$x = \sqrt{v - a}$

(l) $x^3 - 4 = 5y$
Add 4, then take the cube root:
$x = \sqrt[3]{5y + 4}$

(m) $\frac{x + t}{m} = 2c$
Multiply by $m$, then subtract $t$:
$x = 2cm - t$

(n) $\frac{w + x}{u} = 3z$
Multiply by $u$, then subtract $w$:
$x = 3zu - w$

(o) $A = \pi x^2$
Divide by $\pi$, then take the square root:
$x = \sqrt{\frac{A}{\pi}}$

(p) $A = \frac{1}{2}bx$
Multiply by 2, then divide by $b$:
$x = \frac{2A}{b}$

(q) $V = abx$
Divide by $ab$:
$x = \frac{V}{ab}$

(r) $v^2 = u^2 + 2ax$
Subtract $u^2$, then divide by $2a$:
$x = \frac{v^2 - u^2}{2a}$

(s) $\frac{a + b}{x} = r$
Multiply by $x$, then divide by $r$:
$x = \frac{a + b}{r}$

(t) $\frac{5cx}{b} = a$
Multiply by $b$, then divide by $5c$:
$x = \frac{ab}{5c}$

(u) $\sqrt[3]{\frac{x}{k}} = w$
Cube both sides, then multiply by $k$:
$x = kw^3$